Ohhh boy. The gas vs diesel quandary.
As most know I'm a committed gas guy...to a point and try to make my situation workable with a gas powered truck. In your case, with a 7500lb. gvw trailer (1999 carrying capacity which I would think you would hit with 5 kids) and THEN trying to carry 7 people in a truck with associated gear (1000lbs) I think you are stretching a gas engine as you look to the future. Those kids are going to grow...maybe a LOT. Not being ugly but how do you plan on fitting 7 folks in the cab of a truck; even a mega cab?
So just thinking off the top of my head; approx. 975 tongue weight at gvw; 900 for folks per your estimate (that will grow); 1000 in truck = 2875. Looks plenty doable for a 1 ton SRW gas with a payload of 4k or so. But, as Javi asked, what about the NEXT trailer of which it sounds like there will be? That's something to consider with a large family at your stage in the growing process.
I don't know about GM HD trucks and not trying to start a truck brand conversation but was looking yesterday for a possible new truck for myself; Ram 3500 diesel (
). Could not find anything configured like I wanted anywhere close BUT did find a load of Ram 3500 diesel duallys at my local dealership. I'm not in the market for a dually but it m ight fit your plans or not. I do know trying to find the "right" truck equipped like you want on a lot can take a year or more to find....even cross country - btdt. Good luck on the hunt.