Everything about this just--
It's so icky, and it's so dangerous to everyone involved. This is what abuse and manipulation does to people. OP's been trying to shoulder this whole thing themselves. A text message to Izzie honestly speaks a lot about OP's character, the fact that they've gone through so much and they're still trying to just do the right thing for their mom and for Izzie is really honestly admirable. The truth is, this whole situation the father created is so complicated and so manipulative. If Izzie (and OP's mom) can be convinced to talk with a certified therapist who deals with abusive or manipulative relationships, that could be really beneficial.
This is a really complicated situation, and seeking professional help and advice could go a long way in making sure that everyone involved, OP, their family, and Izzie, can get out of this safely.
OP, we've all got your back. We see you, and this situation is nothing you should have had to go through. You've been handling this with a lot of grace and strength.