We have a 2010 Suburban 1500 that tows a 27' trailer, weighing in at about 6500# loaded to camp (5000# dry per the sticker). The Suburban does the job ok. We haul 6 people (four small kids), and are probably about at our sticker limits as far as payload and everything goes. Our Sub has the max towing items on it.
Since the trailer you have is about 1100 lbs heavier, you will probably be pushing the limits on a 1/2 ton SUV a little too far, I would suspect.
The Suburban is a fantastic family vehicle, but probably best suited to a smaller trailer, unless you can find a 3/4 ton (we looked for one, but did not find one optioned the way we wanted).
I would think a kid and 2 dogs would work great in a crew cab pickup, though. If you haven't been in one lately, you should check it out. The back seats are really big and comfortable -- my co-workers comment on the roominess of the rear seat in my F150 every time they get in it. When I drop my kids of at school, there is enough room that they literally stand up and walk out (instead of scooting across the seat to the door). Should you want the dogs in the cab with you, in a Ford supercrew or Ram megacab (and I suspect the others, although I haven't been in a newer GM crew cab lately), there would be plenty of floor space for 2 dogs, particularly with the little one in a car seat.