Would it be possible to go ahead and allow the other kids to go ahead and start enjoying their presents while this one set of cousins continues to open their presents? I mean, it seems ridiculous to me that one family is allowed to monopolize the time of everyone else because their parents are spoiling them rotten (ok, maybe they're not, but it certainly seems like they're doing something like that--or overcompensating). It seems pretty clear to me that at the point where this one family is the only one opening presents, "family" present opening time is over.
Is there a reason why everyone else MUST watch them opening their remaining presents? Is it just so everyone else can Ooo and Ah over their presents with them? Judging from your comment above, you are not going to be able to change the way that family does things. So the only thing you can do is change what YOU and your family do (and I get the whole family politics thing. I have 3 sisters-in-law and 5 nieces and nephews all between the ages of 2 and 6).
Perhaps when it becomes clear that "family" opening is over, you allow your daughter to open one quiet toy/book/whatever that she can play with while her cousins finish opening their presents. The rule is she gets to open one, she can't be loud, and the rest of the presents can be opened once her cousins are done. Or, if you're concerned that just doing it will offend others, maybe looking directly at the cousin's mom and saying,"You know, (insert daughter's name) has been really looking forward to getting x for Christmas. If you don't care, I'm going to go ahead and let her open it while you all finish up."
That way, you're sort of asking permission, but not really. I mean what is she going to say? No, I want to be everyone's focus of attention? If she says that, then there are other issues at play here. I'm not saying you just mentally check out, I'm just saying that you don't necessarily provide them with your undivided attention. Go get some eggnog, check out your presents. Start flipping through that new book you got. Whatever.
Another thought is maybe when family opening time is going on, when you're going around opening presents one at a time, everyone first opens Grandma's gift then Grandpa's gift and so on until all of the presents given sort of universally are opened. That way the only presents left at the end are the ones given amongst that sub-family and no one else feels obligated to watch cause the outside-family gifts are all ready opened. Does that make any sense?