An auto car on a tow dolly?

When I had problems similar to yours it turned out to be the alternator. It wasn't putting enough charging power to the system and it would shut down sensors, tripping different lights on even the anti lock brake light. Just a thought, but when I replaced my alternator the problems stopped.
Tripping on different lights and sensors? That does sound similar to what I'm seeing. Is it anything I can check eoth a multimeter?