We have the exact same family configuration and a fifth wheel - 2 adults, 3 kids and the same size dog. The dog generally goes in a crate in the back of the truck. If it's really hot out, we'll lay a sheet down and flip up the center console and let her ride up front. The back seat floor would be another option albeit a little tight unless you have a Megacab. Honestly I'd be fine throwing her in a crate in the trailer too but I admittedly put the dog on a lower level of importance relative to the humans in our family.
Heavy duty SUV's are old and hard to find at this point, and I didn't want to do one of the heavy duty vans. The newer crew cabs are comfortable enough for 5, imo.
Get yourself fixed because a fourth kid really complicates things.