Your parents are downright evil and have taken advantage of you for a long time, financially and emotionally. This is not about you being trans. This is about them being disturbed SOBs and trying to control you and your wife. Sell the house for as much as you can get to someone else, and get the hell away from them. They are sick.
Your dog is part of your family, and is extremely sick right now. I am so glad he is responding well to the chemo, but that does not alter the fact that he is seriously ill. I would NOT keep him in ANY basement, away from me. This is not coddling, and the people who say shit like that are idiots-EVERYONE who is ill, feels better when their caregiver is close by. Your family will just have to do without you this Thanksgiving. I would not even travel with a sick dog.