The fact that your boyfriend cheated on you with his ex-girlfriend the day after you broke up should give you a good indication of his character. Although he probably justifies his actions by saying that he no longer had a commitment to you because you had broken up, his actions were hurtful.
Now, he wants you back, but your heart is still stinging from his betrayal. Not only does he want you back, but he thinks he can have the best of both worlds: living with an ex-girlfriend (who he has recently had sex with) while dating you.
Problem is you will never really know if he's cheating on you or not, so agreeing to put up with the situation he proposes is just going to cause you more heartbreak and suffering, while he's going to get to have things exactly as he wants them.
I understand that you love him, but who you love is the person you thought you had before he summarily broke up with you and slept with someone else. You have to acknowledge that you can't trust him.
Since the foundation of love is trust, he can't just "get back in your heart," he must earn your trust.
My advice: tell him that this arrangement he proposes doesn't work for you. Then tell him why.
If he wants you back, he's going to have to do the work and endure the scrutiny that will slowly allow your heart to heal. He can't do this while living with his ex-girlfriend since his actions with her resulted in your ruptured sense of trust.
Give him an alternative to his proposal: he can share a place with a male roommate while taking the actions that will help you to regain your trust in him.
Don't settle for anything less.
Regardless of what happens, I recommend that you read this resource which will help you see beyond the words to the character of the person you are dating.
