There is nothing wrong about caring. Caring is a natural human emotion. But please, do not call and offer him your couch. It would just be opening up that whole can of worms again. It's good that he's not accusing or berating you (today), so just be thankful for that. Allow things to progress however they are going to. If you toss that bone to him now, there is no telling where it will lead.
He is a grown man and is perfectly able to find a place to stay. You said offers had been made but he still stays at his job. Bad decision on his part since it could cost him his job. It just shows that he is still not making good decisions and that is not your fault, nor is it your responsibility.
Also don't forget, your girls were scared at your mom's house. They do not deserve to have to live being afraid at night.