Oh Rachel, well done for managing your emotions, in with Sage here, take it so so slow! Sleep in your bed?! Its a no! A day ago he shared someone elses bed!
Get some sleep and take your time, obv listen to him, but do not rush into things. Sage gives sound advice, it is absolutely ok for you to take time to think.
Rachel he has out you through hell, he has shown no remorse, no changes in himself, no respect for you. And in the meantime you have taken time to grow and change, is he the person you want by your side the way he is now?
How long until he cheats again? This isnt just terrible for you, but unhealthy for the kids. He is a grown man and if that means he stays somewhere else for now and can show you that he can be a reliable stable father and a man you deserve then be it like that.
The ball is in your court, i know if didnt feel like it but you are in control of your life and what happens next for you and the kids.