you are not doing anything wrong and you have not done anything wrong. He has decided to cheat (people cheat even when love is not an issue) It sounds like he wants best of both worlds- being with you and being with his ex intimately. That is not a healthy relationship (it is a love triangle) When someone loves another they do not hurt them nor do they betray their trust.
If you find yourself being more unhappy and having to always wonder what he's going to be up to next, it may be a time to sort out your priorities.
You do not want to be the third wheel and what he and his ex are doing does not seem healthy nor appropriate for your relationship.
Him halting the interaction/talking to his, ex is not an issue of not being able to but of his unwillingness level.