
Quoting
Dogmatique
Audio - a bit fat "no". Even if you inform Mom, that does not make it ok to record her without consent.
Video - well, Nannycams are generally ok in every State PROVIDED they don't record audio.
Mom also has a reasonable expectation of privacy in the bedroom and certainly the bathroom. So don't even think of doing anything there. Taping the child might come with other issues, specially if Mom doesn't agree.
If she calls the police, and is able to articulate a fear of bodily harm or just a threat, she may be able to obtain at least a temporary restraining order which would effectively make it impossible for you to stay where you are.