Given she is old enough now to have her own friends to pick that she wants to invite I would have it when best suits you and her! Invite her friends she wants and what ever family can make it good otherwise too bad its her birthday with her friends and if family can't see that they can bugger off!!!!!!!!

Grrr at your SIL thinking attention would be off her DD FFS will be happening for ever now as 2 kids in family have birthdays near each other!!

I hope you can work it out without too much stress.