I see nothing wrong with the parents wanting to give their daughter an extra special.name.for their daughter. . I went to school with a girl.who nearly dided when she was a new born, and because of that her mother named her [name_f]Treasure[/name_f], and she was always very proud of her name. I quite like the name [name_f]Paloma[/name_f] which means dove, [name_f]Matilda[/name_f] which means battle mighty, [name_u]Angel[/name_u] is a super cute name, and [name_f]Elizabeth[/name_f] is always a fantastic classic.
1.) [name_f]Grace[/name_f]- is an obvious one, but with a great emotional meaning. Being graced with her presence, as you are and if she makes it, its God’s grace and he saw her importance here on earth. I apologies if I offended. I’m not for sure in your religious beliefs.
2.) [name_f]Theodora[/name_f]/[name_f]Theodosia[/name_f]/[name_f]ALthea[/name_f]/[name_f]Thea[/name_f] - God’s Gift
3.) Carabella/[name_f]Cara[/name_f]/bella - Pretty face
4.) Emerence/ [name_f]Emmy[/name_f]/[name_f]Emma[/name_f]- [name_m]Worthy[/name_m] of Merit
5.)Belicent/[name_u]Bell[/name_u]/[name_f]Bella[/name_f]- Biblical, which means merciful and gracious
6.) [name_f]Bethia[/name_f]/ [name_f]Beth[/name_f] - Biblical, daughter of God
8.)[name_f]Aurelia[/name_f]- means golden
9.) Serephina/[name_f]Sera[/name_f] like [name_f]Sara[/name_f]-it means firey one- She has to be to have come thus far
10.) [name_f]Eveline[/name_f]/[name_f]Evelina[/name_f]/ [name_f]Eve[/name_f]- means life
11.) Ismerie/[name_u]Izzy[/name_u]/[name_f]Issie[/name_f]- commonly refered to as Notre Dame de Liesse , Our Lady of Liesse, or more directly “Our Lady of [name_f]Joy[/name_f].” St. Ismerie.- name mean protection/supreme
12.)[name_f]Alba[/name_f]/[name_f]Ally[/name_f] - it means white but can be construed as pure from darkness
13.) [name_u]Juniper[/name_u]/[name_u]June[/name_u]- it means young sprout or youthful sprout-fun quirky and sets her apart in names compared to her brothers
14.) [name_f]Jenica[/name_f]/[name_f]Jenna[/name_f]- means God’s gracious gift
15.) [name_f]Orabel[/name_f]/Oranella/[name_f]Arabella[/name_f]/[name_u]Ara[/name_u]/[name_f]Belle[/name_f]- means yeilding to prayer and many princesses have been given this name
16.) Dulcebella/[name_f]Dulcie[/name_f] as a nn or full name- Italian for sweet
17.) [name_f]Doveva[/name_f]/ or [name_f]Dova[/name_f]-nn… [name_f]Dovie[/name_f]-- the bird which means/represents peace and strength
18.) [name_f]Adelaide[/name_f]/[name_f]Addy[/name_f] - noble one
19.) [name_f]Imogen[/name_f]/[name_f]Gen[/name_f]- beloved child in celtic
20.) [name_f]Olive[/name_f]- symbol of peace
22.)[name_f]Pearl[/name_f]- represent beuaty and splendor
23.) [name_f]Juliette[/name_f]/Juls/[name_u]Julie[/name_u]/[name_f]Etta[/name_f]- means youthful
24.) [name_f]Tansy[/name_f]- this one is a littlebit off beat, its florigraphic meaning (meaning of the floral bouquet given) is “I declare/challenge war on you.” It may seem precocious at first, but she seems to be a fighter, so it could be seen appropriate! 
25.) [name_f]Rebecca[/name_f]/[name_f]Becca[/name_f]/[name_f]Becky[/name_f] - servant of God
26.) [name_f]Primrose[/name_f]/[name_f]Rose[/name_f]/Prim/Primmie- means first [name_f]Rose[/name_f]-florigraphic meaning is youthful innocence
27.) [name_f]Liberty[/name_f]/[name_f]Libby[/name_f]- its a virtue name
28.) [name_f]Faith[/name_f]- “[name_f]Faith[/name_f] is one of the most straightforward of the virtue names popularized by the Puritans in the seventeenth century, many parents still choosing it as an indicator of their religious conviction.”
29.)Vesperina/[name_f]Vespera[/name_f]/[name_u]Vesper[/name_u]-nn [name_u]Vesper[/name_u]/Vessa/[name_f]Essa[/name_f]- evening star and evening prayers- the star reminds me of the star of Bethlehem-nice meaning but still off beat
30.) [name_f]Eugenia[/name_f]/[name_f]Genie[/name_f]- means wellborn
32.) [name_f]Eulalia[/name_f]/[name_f]Lalia[/name_f] nn- means sweet spoken one
33.) [name_f]Prunella[/name_f]-nn. prue. means small plum
34.) Engelieth-Engie nn- Old [name_m]German[/name_m] form for Angils- which means [name_u]Angel[/name_u]- leith is gyd for old English- it means war. The whole name translate out to fighting with (not against) the angels. It gives the a poetic meaning- she is fighting for her life and the Angels are among her. Pronounced: Eng-eh-leeth (more American/french sounding) or Enge-lie-eth or En-Gil-eeth
35.) Ivelisse- [name_f]Eve[/name_f]/[name_f]Evie[/name_f]/[name_f]Ivy[/name_f]- means life with a ethereal/evocative feel
36.)[name_f]Isabeau[/name_f] (IZ-ah-bow, EE-zah-bow) is a [name_m]French[/name_m] variant of [name_f]Isabel[/name_f], derived from the Hebrew name [name_f]Elizabeth[/name_f] ([name_f]Elisheba[/name_f]/[name_f]Elisheva[/name_f]), meaning “God’s promise, my god is a vow/oath.”
37.)[name_m]Tobin[/name_m]/[name_f]Toba[/name_f]/Tobina (TOH-bihn) is a Hebrew name meaning "God is good
38.) [name_m]Palmer[/name_m] is an Old English name meaning “palm-bearing pilgrim,”
39.) [name_f]Christabel[/name_f]-the [name_m]French[/name_m] name [name_f]Christabel[/name_f] is a coinage combining “[name_m]Christ[/name_m]” with the -bel suffix to mean “beautiful [name_m]Christian[/name_m],”
40.) [name_f]Susannah[/name_f]- The original Hebrew version of the name was [name_f]Shoshana[/name_f], meaning “lily.”
41.) Belina- Belina and [name_f]Bellina[/name_f], primarily used in Spanish and Italian, mean “beautiful” and are typical variants of [name_f]Bella[/name_f]
42.) [name_f]Evangeline[/name_f]- Origin: Greek (and Cajun/Acadian), meaning “bearer of good news.” It was invented by [name_m]Henry[/name_m] Wadsworth [name_m]Longfellow[/name_m] for his Acadian epic poem, “[name_f]Evangeline[/name_f],” although the events of the poem really happened in reality during the Acadian Expulsion. [name_f]Evangeline[/name_f] derives from the Greek word euangelion, evangel, the term for the gospels, and Latin evangelium.
Popularity: In 2010 there were 20 baby girls named Evangaline, 12 [name_f]Evangelene[/name_f], 30 [name_f]Evangelia[/name_f], 9 Evangelin, 188 [name_f]Evangelina[/name_f], 953 Evangelin,28 [name_f]Evangelyn[/name_f], 8 [name_f]Evangelynn[/name_f] and 953 [name_f]Evangeline[/name_f], ranking at #333, her highest ever until 2011, rising to #286 with 1,099 births.
I hope this helps. God Bless! 
Lionella/[name_f]Ella[/name_f] nn. [name_m]Jac[/name_m]/[name_m]Zak[/name_m]/[name_f]Ella[/name_f] -
Today’s names: [name_u]Lionel[/name_u] & Lionella
For most [name_m]Lio[/name_m]/[name_m]Leo[/name_m] names the “i” or “e” is interchangeable. [name_u]Lionel[/name_u], [name_m]Leo[/name_m], [name_m]Leonard[/name_m], [name_m]Leopold[/name_m], etc. Lionella, [name_f]Leona[/name_f], etc.
Pronunciation: [name_m]LY[/name_m]-on-ell, [name_u]LEE[/name_u]-oh-nell-uh
Potential nicknames: [name_m]Lio[/name_m], [name_m]Lion[/name_m]; [name_m]Lio[/name_m], [name_f]Liona[/name_f], [name_f]Nella[/name_f], [name_f]Ella[/name_f], [name_f]Ellie[/name_f]
Origin: English variant form of Latin name [name_m]Leo[/name_m], meaning “lion,” but the -el ending makes it mean “little lion.” Lionella is the female Italian variant
I really like the suggestion of [name_f]Eve[/name_f] and think it goes perfectly with your boys names.
Some other suggestions:
[name_f]Phoebe[/name_f] - “radiant, shining one”
[name_f]Annabelle[/name_f] - “loving”
[name_f]Leah[/name_f]
[name_f]Audrey[/name_f] - “noble strength”
[name_f]Virginia[/name_f] - “virginal, pure”
[name_f]Mira[/name_f] - “admirable”
[name_f]Claire[/name_f]/[name_f]Clara[/name_f] - “bright, clear”
[name_f]Lydia[/name_f]
[name_f]Jane[/name_f] - “god’s gracious gift”
[name_f]Celia[/name_f] - “heavenly”
[name_f]Louisa[/name_f] - “renowned warrior”
[name_f]Cordelia[/name_f] - “heart, daughter of the sea”
[name_f]Marigold[/name_f]
[name_f]Nora[/name_f] - “light”
[name_f]Caroline[/name_f]
Out of these, I think I like [name_f]Claire[/name_f], [name_f]Nora[/name_f], and [name_f]Phoebe[/name_f] for you. Good luck with everything 
I second [name_f]Audrey[/name_f], [name_f]Hannah[/name_f], and [name_f]Matilda[/name_f].
Some that come to my mind:
[name_f]Bernadette[/name_f] - “brave as a bear”
[name_f]Aveline[/name_f]
[name_f]Marianne[/name_f]
[name_f]Celia[/name_f] - heavenly
[name_f]Zelia[/name_f]
~~ Sending Lots of [name_f]Love[/name_f], Hugs & Prayers ~~
Some suggestions for your precious baby girl (as a FN or MN):
Blessing
Bless
[name_u]Bliss[/name_u]
[name_f]Miracle[/name_f]
Courage
[name_f]Hope[/name_f]
[name_u]Ever[/name_u]
[name_f]Cara[/name_f]/[name_f]Carys[/name_f]/ [name_f]Caris[/name_f] (dear, love or beloved in Welsh)
[name_f]Rose[/name_f]
Beauty
[name_f]Belle[/name_f]
[name_f]Isabelle[/name_f]
[name_f]Joy[/name_f]
[name_f]Zoe[/name_f] (means life)
[name_f]Vivienne[/name_f] (full of life)
[name_f]Angelica[/name_f]
[name_f]Epiphany[/name_f]
[name_u]Ruby[/name_u]
[name_f]Mia[/name_f] [name_f]Rose[/name_f] (my rose)
[name_f]Gardenia[/name_f]
Best Wishes & Miracles xxoo
Another idea I had was [name_f]Freya[/name_f] - a very fierce and strong goddess from Norse mythology. Some friends used it for their baby daughter who was born incredibly premature with terrible odds, but is now an eighteen year old about to start University. They wanted to give her a name that symbolised the strength she obviously had to pull through.
Very best wishes, we are all thinking of you and your family.
I like the previous names of [name_f]Hannah[/name_f] and [name_f]Hope[/name_f]. [name_f]Asha[/name_f] means hope, and [name_f]Arabella[/name_f] means yielding to prayer, So those seem like good options also
[name_f]Elianna[/name_f] meaning my God has answered
[name_f]Chava[/name_f] or [name_f]Eve[/name_f] meaning life
[name_f]Abigail[/name_f] my fathers [name_f]Joy[/name_f]
[name_f]Aliza[/name_f] joyful
[name_f]Hannah[/name_f] grace
[name_f]Talia[/name_f] dew of heaven
These are all Hebrew to go along with your sons names
I’m sorry you are having to experience this,i think a name with a meaning of [name_f]Joy[/name_f] would be lovely,
Thank you all, some really great options there. [name_m]Will[/name_m] let you know what we pick out
I like [name_f]Zoe[/name_f], or any other name that means “Life.” But especially [name_f]Zoe[/name_f]. (I think [name_f]Eve[/name_f] is a little heavy in this situation).
You are not defining her by her illness. You are affirming that she is a life, however long that life may be. The idea of “life” is not about time. It’s not about hope or healing or anything else. It’s about her, and that she is a life and has a life. And the name [name_f]Zoe[/name_f] is adorable. [name_f]Zoe[/name_f], [name_m]Zack[/name_m], and [name_m]Jake[/name_m] works.
So sorry for your situation. And if your little girl does not survive long, I wish you much comfort and joy in watching [name_m]Jake[/name_m] grow up.
I ditto the suggestion of [name_f]Zoe[/name_f]. It means life.