Ahh, the myth of the sport-utility vehicle: Half my neighbors own them, and about half of those were surprised that the payload was no higher than that of an average sedan or minivan.
But just in case you don't want to read my moralizing: I've carried four adult bikes on my Yakima roof rack on a Honda Civic coupe, where you can only get the towers about two feet apart. I doubt it's recommended, but I've gone tens of thousands of miles that way with no problems, and if I had to, I wouldn't be afraid to wedge another bike in there. I suspect the weight limit is based more on how the topheavy car handles than on the physical limits of the rack. Didn't bother the Honda much if I drove it gently, but SUVs are generally topheavy and handle like crap anyway, so don't go whipping through the esses like a Lotus. Install the rack carefully, and check often to be sure nothing's coming loose or sliding back. There's a lot of drag on that load, and the rack will slide off and go bouncing down the road if you don't do it right. Your mileage will plummet, too--the Honda gets about 34 hwy without the rack, 31 with a bare rack and mid-20s with bikes up.
Suggestions, not necessarily helpful:
If the rack uses fork mounts, put the front wheels inside rather than on top. Leave some stuff home to make room; you're taking more than you need anyway.
Remove all the bags, pumps, etc. Sounds obvious, but i see people all the time with panniers on the bikes on the rack.
Drive like you had good sense. You'll have a lot of weight waving around there on the end of a lever, and it will affect the handling of the car. Don't get into emergency situations and you won't have to get out of them. In my experience this isn't a huge problem, but you CAN feel it.
On my Mazda, I've carried three bikes on the rack, one on a trunk-mount rack left over from the '80s and one, wheels off, inside. That means your daughter will have to leave her big makeup case at home.
Haven't checked prices lately, but you can probably rent a small trailer from U-Haul fairly cheaply that would solve all your problems.