I am going to try very hard not to feel the need to defend our actions in the situation. Obviously if it were as easy as this, it would not have been a problem. The little girl in tears before she had even waded through half of the gifts in the final stop was of much more importance to us than carving out time to have her open our gift. Since half of the gifts were not open, my kid was in tears, and there was a bunch of relatives waiting to see her get to their gifts, all bets/plans/sanity had left the room. We did not expect people to "make a special time" for it. Again, obviously, since our families did not even know about it we were not expecting them to do such a thing. It is just very sad that the piles of gifts, the time it took to open them, and the resulting meltdown created a situation in which we were not able to enjoy the act of gifting our own child one gift on Christmas. Is that really hard to understand?
My niece and nephew are the ones with the giant gift piles (1st of each gender for my parents). They're the ones that have been in tears about Christmas presents and whose parents sat there and didn't try to teach them anything about graciously accepting gifts. But those times are long gone. My parents now spend the same money they used to spend on 1 or 2 grandchildren on 10 and my kid will never be there. And that sucks. She's so far down the line of grandkids that no one could care one little bit about her on Christmas. Her birthday is pretty much the only time she gets in the spotlight at all, but she shares even that. And my family doesn't think birthdays are important.
Our position is so far from yours that I really can't understand where you are coming from. I would LOVE for my kid, just once, to be given more presents that she wants to open.