As you say, your sister will make the final decision. Have you brainstormed with her ideas for how to get it to work out so you can care for her in your home?

I think if your father behaves badly in this last drama, you and your brother are not going to want to reconcile with him; I think you and your brother should talk together and put some pressure on your father, make sure he knows this; that his actions in the next few weeks and months will have consequences. Maybe you and your brother can get some sort of schedule going where your father agrees to come visit your sister at your home and only then present that arrangement to your sister so she is not conflicted about coming to live with you?