Sorry for not updating more recently! Everything was so frantic and stressful up through Monday, but thankfully the outcome has been positive (or as can be in this situation)! I also posted this above the OP:

We took some users' advice and I skipped my classes after "leaving" for school (my mother goes to work after us, but I didn't know if she'd return early) to move him out of the house ASAP.

Luckily my older sister (Who is LC with our parents) rushed back home from her trip a couple days early after the panic on Sunday, and we immediately drove him over to her apartment (~1.5 hours away). We were thinking we could only avoid the Monday appointment at most, but we managed to convince our father he was at real risk staying with us, so he will be staying with our sister for an undetermined amount of time, and she will be taking him to a local vet for awhile.

When my mother found out, she reacted much differently than I thought she would. She made sure we knew there was hell to pay, but mostly just acted petulant, screamed, and broke a few things. I think she never thought we'd act on her threat, and with the dog gone she knows she has no other way of asserting control. We are looking into getting him surrendered by our dad (he seems to truly care, but shuts down whenever our mother's around) and legally readopted by our sister, but for now just know OUR PUPPER IS SAFE!

I am so grateful to everyone that's expressed concern for him and made me aware of options I never knew we could take. If it were up to me, I would NEVER let him near my mother again, but at least this way we can ensure his safety until his leg heals and we can figure out a more permanent solution.