If one of your kids needed your exclusive attention for an hour (barring emergencies, of course), really, the other one could not handle it? I'm not saying that they have to be *happy* about it, but they honestly could not handle their sibling getting undivided attention for an hour or an hour and a half, once a week? When they also get some family time, AND they know they will get their undivided attention time? I don't know, I think that is not too much to ask of 7 year old and up (though if it's *never* been done, that would be really hard at first I'd think). Though maybe it it just easier in our family becase we have very flexible schedules (DH is a WAHD) and again, it's a habit by now, we're not introducing the concept at this age. And we also have a ton of time together as a family.
I like the divide and conquer strategy that limabean speaks of, if you can swing it (actually, DH and I have noticed that it works well even with 3...because there is definitely a different dynamic when you have one of the sibs removed. Esp. now that DD is starting to pull away in interests from her brothers after so many years of having pretty much the same interests and likes, having some one on one sib time seems to be something they enjoy too, though for the most part my kids are very close to each other even if they squabble, so maybe that would not be the case with other sibs).
I've had several times where I needed over an hour of private conversation to help a child work through something big at school or in their lives, even though it wasn't a fun movie night. When that has had to happen, my kids have been respectful of their sibs need to have that time, it was really nice to not have to worry about siblings freaking out at the same time. I don't know if that's because they know that they all get their time, so they're more tolerant of that sort of thing, or they are used to me enforcing "hey, right now I need to spend some time with sis/bro, unless it's an emergency it will have to wait" thing, or what, but as my daughter in particular starts moving into puberty and other changes, I am seeing dividends being paid in the one on one time that DH and I have both invested in her and in the respect for one on one time on the part of the others.