I’ve been looking for a name to replace my favorite, [name]Lucy[/name]. (Familial harmony keeps me from using it.) [name]Vivian[/name] seems to hit the same sweet spot. It does not have husband approval yet, so this might be all for naught, lol. My questions are:
What do you think of [name]Vivian[/name] and its variants? [name]Vivian[/name], [name]Vivia[/name], [name]Vivien[/name], or [name]Vivienne[/name]?
Which would best suit, if any, a sister to my children, [name]Caleb[/name] and [name]Annabel[/name]?
Lastly, I adore the nickname [name]Vivi[/name]. If husband does not approve [name]Vivian[/name], et al, are there any other options to get the same nickname?
Thank you!
[name]Violet[/name] nn [name]Vivi[/name]?
I love [name]Vivia[/name] and [name]Viviana[/name] (and [name]Vivienne[/name] is pretty cute too) but they seem a little harsher and more grown up than [name]Annabel[/name]. [name]Annabel[/name] and [name]Violet[/name] is a great fit though!
If not how about:
[name]Viola[/name]
[name]Vida[/name]
[name]Vita[/name]
[name]Vina[/name]
[name]Vieira[/name]
[name]Viera[/name]
[name]Victoria[/name]
[name]Vienne[/name]
[name]Vienna[/name]
I think any name starting with [name]Vi[/name] could have [name]Vivi[/name] as a nn!
I also think [name]Genevieve[/name], [name]Sylvie[/name] or [name]Sylvia[/name] nn [name]Vivi[/name] could possibly work.
[name]Hope[/name] that helps, and of your choices I think [name]Vivienne[/name] is the best sibling match for [name]Caleb[/name] and [name]Annabel[/name]. [name]Lovely[/name] names by the way 
Your children have such wonderful names! I love [name]Annabel[/name], my friend recently had a little girl and named her this, and my brother’s name is [name]Caleb[/name]
I think ljandrl had some AMAZING suggestions about how to get to [name]Vivi[/name]. Although I personally prefer the [name]Vivian[/name] spelling of the name (it’s my 3rd favourite girl’s name) I like it best because to me [name]Vivia[/name] feels incomplete, it is more familiar and therefore less likely to be spelt incorrectly than [name]Vivien[/name], and the extra ‘ne’ on [name]Vivienne[/name] has always seemed just a tad pretentious to me (unless of course you’re French) But that is all personal opinion. I think they’re all fabulous choices and would work well with your other childrens names.
Here are a couple more suggestions (some of which are a little more exotic) to add to ljandrl’s list
[name]Vivica[/name]/[name]Vivika[/name]
Virika
Vian
Vianca
Vinata
Vinaya
[name]Vinita[/name]
Visala
Visola
[name]Viva[/name]
Vitalia
[name]Vivianna[/name]
Also [name]Olivia[/name], [name]Livia[/name] and Liviana include ‘vi’ And you could possibly get away with [name]Vivi[/name] as a nickname for [name]Ivy[/name] (one of those cases where the nickname is longer than the actual name!)
I hope you find something both you and your husband like! 
I prefer [name]Vivia[/name] and [name]Vivienne[/name]. girly,floaty and pretty
I prefer [name]Vivienne[/name] as it’s French and just looks more feminine and is lovely to the eye and ear. I also like the [name]Vivien[/name] spelling, I suppose because of [name]Vivien[/name] [name]Leigh[/name]
For [name]Viv[/name] I think [name]Genevieve[/name], [name]Vienna[/name], [name]Viola[/name], & [name]Violet[/name] are all possibilities.
I would prefer to see [name]Viviana[/name] if I had to chose a [name]Vivi[/name]- name. I still like [name]Vivienne[/name] quite a bit, though. As for [name]Vivi[/name] as a nn, [name]Aviva[/name] nn [name]Vivi[/name] would rock my socks!
Thak you all for the great feedback and suggestions! Unfortunately, my husband is not buying [name]Vivi[/name]. On the upside, he’s decided that he loves [name]Maisie[/name], which is also one of my favorites! Now to find the perfect middle name.