Does your W have a court order to keep you out of the marital home and away from the dog? If not, it's not legal according to CA law to deny you access, from what I understand. Did you interview more than one L? Did you get someone who specializes in D?
I'm very sorry about the situation you find yourself in - it must be very draining to also have your ailing mother to take care of. Can you not get part-time care for her through her insurance or Medicare? There should be opportunities for both respite care and home health services that are covered.
Think about this as putting on your own oxygen mask - you need to take care of yourself so you can take care of her.
Your WW's distortion of the relationship history and complaints about you is completely normal - well, not normal but common. It's the only way they can defend to themselves what they're doing. Don't take it personally at all (unless you truly feel she has a point and it's something you can change).
Best wishes!
M 16 yrs, WH62, P54 3 adult blended kids EA 11/13, BD1 6/14 PA fall 14, BD2 2/15 Piecing 2015, BD3 12/15 Separated 4/16 WH moved OW in 5/16 Divorced 6/15/17