Lots of good advice OP and seeing that you're more interested in a used vehicle, then I'll agree too that a 3/4 ton van should be had. They are out there. Used CC pick-ups are not as large as say '17 and up are. Tho a Forde guy, the Mega cab is HUGE inside, but as OP said, they have 3 little ones and a dog, so the dog would end up on floor or in crate in bed of truck as one poster said if truck is a CC.
So OP, do a used 3/4 ton van search unless you see the need to have a pick up for other things. Also, plan for several years down the road as vehicles prices are going nuts, your needs and all. On a personal note here, we bought a '15 F350 CC SRW in Dec of '14 thinking no problem as it had high tow numbers across the board. 2 years later we upgraded RV (in sig) and now we are at max and then some with weights. She did ok 1st year ('15 F350) and I really liked the truck. Come '18 vaykay plans to FL in summer time. Knowing we were over on tire capacity on the '15, had this nagging/gut feeling that wouldn't go away. So ended up getting a '17 F350 DRW. She tows like a dream, wife is more comfy driving / the RV while I catch a nap. Do I like the DRW? For towing yes. Would I like a SRW instead, yes---especially in winter. Pocketbook only goes so far and while the newest of trucks all have higher ratings, the weight of the RV is dictating type of truck and to feel safe in. Like I said, the '15 did well but it was up against all the ratings for it. If a tire blew on it at Hiway speed and the weight she had..........YEE HAW ! Being wise on the yeehaw haw. Wife does well when she's driving/towing and for her to say she feels better w/ the DRW while towing, well that says it all and now feel better about going/getting the DRW. Just something to think about.