If you think about it realistically, about 90% of party food which is served up will have some element of dairy in it - sandwiches with butter, cakes and biscuits are all going to contain it, and that's even before you get to the jelly and ice-cream - you might be lucky to get away with the crisps but that's not guarunteed!!
My DD is allergic to egg and milk and I have to say that I would not expect a stressed out party Mum to fully cater for her. Her child will, in any event, no doubt want her favourite things at the party. What I do which works well for us is speak to the Mum, find out what sort of food they are going to have and send my daughter along with something similar, eg sandwiches, biscuits etc which I know are safe for her to eat. I often find that Mums will then gratefully meet you half way - eg keeping jelly and fruit completely separate from ice cream etc, supplying safe drinks and easy stuff like that so my dd can join in to a certain extent and then just empty her own "safe" food out onto a clean party plate for the rest.
It's tough on your dd I know not to be able to join in with everything but I have found that at least this way I know my dd will not eat anything inappropriate!
Good luck with it. I hope you find a solution.
Coral