What a sad situation.
Did the doctor prescribe an anti-depressant for your father-in-law?
It sounds like a nursing facility is probably the best place for his wife to be, but her doctor should have been able to give her something to calm her aggression.
I can understand why he is depressed and struggling with guilt, not because he placed her in a facility, which definitely seems like the right decision, but because he is so far away from her. He probably misses her, is very worried about her, and feels that he abandoned her. I imagine those are pretty normal feelings under the circumstances.
If you can find an Alzheimer's support group, that could be a big help to all of you. Guilt is, unfortunately, something that a lot of spouses and family members deal with.
Would it be possible for him to move back home, and make arrangements to prevent him from being able to remove his wife from the facility? That way, he could at least visit her and it would probably help ease some of his depression and guilt.
His wife will almost surely settle in where she is, and will probably be quite content there, but it can take some time. If he can just hang on a while, they can both adjust to the new situation. It must be really hard for him to be so far away from her.
Some other people here may have more suggestions for you. In the meantime, I think an Alzheimer's support group could be a good place to start.
Good luck. I hope you'll keep us posted.
Carol