First of all, forget about overcoming everyone's objections to your situation.
Concentrate on you and what you need out of a relationship.
The first need would be a man who can be true to you. Yes? Well I believe you already know this but this guy is not being true to you. He is playing you like the proverbial fiddle. There is absolutely no reason why he would have to live with his child's mother in order to take care of his child. Personally, I would have a conversation with the childs mother and then change the locks on my door...okay, not necessarily in that order.
Before you get into another relationship make a list of things you want out of it and the way you want and do not want to be treated and then hold your ground. If someone violates your boundaries give serious consideration to dumping them.