It sounds like your plans are well thought out and you have already considered most options.
Has the dog already ridden in the 5er? The way you describe the situation makes it sound like it has.
My wife has ridden in our 5er (once) when we moved in the campground from our camping site to the trailer dump station. She said the dogs were freaking out due to the movement and noise in the trailer. That would be my biggest concern - a traumatized dog may not be a very good service dog (or companion dog for that matter).
The only other option that you didn't mention was a DRW RAM 3500 MegaCab. I am not sure if it would have the payload/towing capacity, but if it did, the dog could ride on the floor in the rear of the truck, with the three kids in the seats.
Good luck with whatever you decide.