Sounds like you have everyone telling you, your daughter, your mum, but at the end of the day it's your choice.
You asked us so we are now chipping in. Lots of people have said lots of common sense here. I agree that if you really want to change it then you should but I would just think a bit more about it before you make the move.
I agree that Elizabeth is a lovely, pretty and very versatile name. I would say the most versatile, so many possible nicknames for her to choose when she is older and for you to choose now, her nick name does not need to be set in stone. She could be Betsy or Lizzie. I love Betty.
Kitty is OK but I think it does make me think of cats and so does Tabitha a bit so agree that together not so good as her official name but ideal for her sister to call her that.
The trouble with Kitty (IMHO) is that if she does not like it she can't change it, or she can but that would be more confusing - and Elizabeth has so many nicknames.
Agree with whoever said Kizzy, sounds like Lizzy (which is short for Elizabeth) but keeps the Kitty sound your older daughter likes.
Having had a baby and with another at home you might be tired/hormonal so do think carefully before you make the decision.
At the end of the day, your choice for now but be aware she might end up using her own nickname anyway, and she will probably grow into her name as time goes on.