The only thing about taking the PC is that any accounts that have 2 factor authentication(I think that's basically every bank), will likely require a new code if you move it to a different IP address. If your father can provide those codes to you, I'd say just take the computer when your brother isn't around.

You may also want to try adult protective services since your brother seems not to be able to care for himself and is in a bad living situation. They probably aren't equipped for immediate help, but at least they'll be staffed with empathetic people who will know more about your local services.

I'm so sorry you're going through this. I wish I had more specific advice to give you.

I hesitate to write this last bit, but I wish someone had told me when my father got sick and I was the child that had to handle everything:

You're doing the right thing and you're a good person for doing it, but take care of yourself as well. There may end up being times when you need to step back for your own health and mental well being, if so, you're not a bad person. You can't help anyone else if you destroy yourself.