When I was growing up, opening gifts was a part of the party. We continued that practice with our children. The gift isn't a ticket in the door to the party that is handed over and not seen again before leaving.
It also helps instill in the recipient and the giver good life skills and manners. The children giving learn to appreciate the joy of someone liking what they were given, and the pride in being giving. And how to graciously say "you're welcome". The recipient learns how to be a gracious receiver, (whether she has it already or not), and has an opportunity to thank the person right then and there.
To be proper, choose one:
A) your child opens the gift and thanks the giver in person at the party, or
B) your child sits and writes thank-you notes to everyone the next day.
The bigger issue I see with what it sounds like you have planned, is that you have a joint "friends/family" party for a 3 year old, with too many friends.
At 3, having 12 kids is just overwhelming. I always heard that the appropriate number was the age of your kid plus one, so in your case, 4 kid guests. Not 12. When my son turned 5, he had 9 kids in his entire preschool class (K4 class), so we of course invited them all. 7 plus an older sibling came. It was about right.
And of course your daughter's grandparents want to see her open their gifts! But that should probably be reserved for a family gathering, not the one with all the playmate/kids there.