We've had this situation heaps of times over the last 18 months and I always take the other DD (and now DD3) but pay for her in the play centre/Hungry Jacks or whatever to enter and buy food etc for her from the cafe. Whoever wasn't invited also knows that they are not part of the party and therefore don't go in the room, have the food, cake, games etc

TBH I think its rude to ask if siblings can join in the party, even if you do offer to pay. One of my DDs it wouldn't have mattered in terms of her temperament how many kids crammed into the party room at the play centre she chose (although space would have been an issue as we were close to the centre's numbers limit), but DD2 had a party this year and she chose only a handful of kids from her kindy class because emotionally she just can't cope with lots of kids around her, especially ones she doesn't know. I would have been really upset if her day was ruined by uninvited siblings.

I stay for parties at this point, although I think DD1 is getting to the point where she would be ok if I left - not sure I would be though because its rarely just the party kids at play centres