We always wait until the actual birthday to give our kids their gifts. It doesn't matter if they have a party with their friends or just the family party, the gifts from mom and dad don't get opened unless it is their actual birthday. That is why they are called birthday presents not "any day" presents.
Now, I have to say wow.
I have never heard of kids parties being so short that there is no time to open presents. That seems silly.
Isn't the point of a kids birthday party for there to be games, food (whether it's just cake and ice cream or an actual meal) and presents?
It must be a location thing.
The birthday parties my kids have gone to last more along the lines of 3 and 4 hours and the kids are always the ones asking if the birthday kid can open their presents yet.
Then again, most people I know think having a birthday party at a venue is ridiculously expensive. Around $200+. For double the time and half the cost, I'll have the parties at home and have plenty of time for the kids to have fun and eat AND open their presents.