I doubt that your Mom would have made these kind of decisions for her family. I'm sorry & this is harsh, but I think your Dad is thinking with his dick. I don't think I would even let him know what I was doing as far as getting help for your sister. He may try to stop it, since he feels he would be more off the hook if she is institutionalized. I doubt that he is thinking of her well-being, just his. Definitely, contact an attorney. I'm sorry, but I feel so pissed off at him. You don't just throw away your family like this with no regard to their feelings & their lives. So he wants a 2nd chance to be happy. Sounds like he will do anything to have this with no regard for his children.
I don't have any advice, but my heart goes out to you and your sister. I think talking to a counselor or atty would be helpful, at least to give you some options. Maybe they can even tell you that if your dad does not care or financially support your sister, that he is giving up his "rights" to her so to speak, and you can petition to become her guardian.
On the other hand, the assisted home might be worth looking at-they are equipped and trained to help people like your sister.
What do you during the day? do you work? who watches her now? if she's in school now, what happens during summer or after she graduates? are you prepared to put your dreams and goals aside to care for her until you are no longer able to? these are just some things you have to be honest with yourself about, and also consider what is best in the long run for your sister.
I truly respect and admire your devotion to your sister, but you have to look at all angles and do what's good for you as well.