Negative on that. The BB would "step" on the Volvo's brakes but those brakes but those wheels aren't on the ground with the Dolly.
All you need is a Dolly that already has its own set of Brakes. You can get them with Surge brakes. Those are hydraulic, where the "stepping" on the brake occurs as the dolly pushes forward against your coach as you step on the coach's brakes. Rental trailers and many boat trailers work that way. Or electric brakes like most travel trailers and fifth wheels have. Just install a Brake Controller in your coach.
Just don't get a Dolly without brakes. Those are available too. You COULD add brakes to one, but it makes more sense to start out with the right kind.