I'm visiting my parents at the moment and I asked my mum what she thinks. She agrees you should go!
If your sister is genuinely keen to show off her niece you should at least let her know your concerns and see what she says. It's her birthday and if she's up for it why not?
You could have a lovely afternoon, with your DD being entertained/cooed over by her aunt and various friends, you might even get 5 minutes to relax! and if it's awful you can always leave.
Why not take a risk, your DD might give you a pleasant surprise! Just think of how pleased you'll be if you have a nice day.
From my limited experience of such places, the staff make you feel very welcome, even if you are with a child.
And anyway, as my mum says really posh people expect to be able to take their DCs anywhere and for everyone else to put up with it even if they do scream the place down
Sorry to go on about it but I feel really strongly about this kind of thing, because one of my best mates worries so much about how her DS will behave that they never go anywhere unless it is specifically for kids. They are missing out on so much. Despite wanting to go, they have missed out on countless weddings, trips with close friends (and their kids) to restaurants, family holidays (the train journey there was the problem in that case) etc. And as time goes on, my DS is getting used to being in these kinds of places, I'm growing in confidence about where I can take him and he's learning how to behave. With my mate it's becoming a bit of a self-fulfilling prophecy as her DS never gets to have these kinds of experiences. How will he ever learn how to behave in adult company?
FWIW my tips for keeping DC happy in restaurants etc are don't forget to bring lots of toys; don't be afraid to leave if it doesn't work that time; encourage the other adults to interact with your DD, and even entertain/look after her for a while if willing (some people actually LIKE children you know!).
Right, rant over!
HTH