How do I explain to my father-in-law that we didn't exactly sign up for this and he needs to be in an assisted living home?

This is common but hard. Is there an old friend or a third party who can help him understand that you aren't abandoning him, but that it's better for his health and safety to be in AL. Most people fight them move, but many of them love it once they adjust. A third party can often help (even a faith community leader), as there isn't that family dynamic that gets in the way.

Good luck and best wishes. I know it's hard.
Carol