Middle name options:
[name_f]Annie[/name_f] [name_f]Joy[/name_f] (keeps the J theme but no family significance)
[name_f]Annie[/name_f] [name_f]Elizabeth[/name_f] (named after me but no J theme)
[name_f]Annie[/name_f] [name_f]Jerrica[/name_f] maybe. [name_f]Annie[/name_f] [name_f]Elizabeth[/name_f] could be [name_f]Annabeth[/name_f] which is kinda cute as a nickname.
I like [name_f]Annie[/name_f] [name_f]Elizabeth[/name_f] (especially given the significance for you) - I agree that you don’t need to have a J initial.
Both [name_f]Annie[/name_f] [name_f]Joy[/name_f] and [name_f]Annie[/name_f] [name_f]Elizabeth[/name_f] are gorgeous, but I prefer [name_f]Annie[/name_f] [name_f]Elizabeth[/name_f]. [name_f]Annie[/name_f] is so spunky and cute, and [name_f]Elizabeth[/name_f] is classic and elegant. I love that she’d be named after you, and I like a longer middle with [name_f]Annie[/name_f].
Nothing wrong with [name_f]Annie[/name_f] [name_f]Elizabeth[/name_f] but I prefer [name_f]Annie[/name_f] [name_f]Joy[/name_f]. It has a playful feel to it, very uplifting.