He's in an awesome position and is trying to weasel out of changing. Bullshit that he cares about her feelings. She is the other woman and I'm sorry but her feelings mean a lot less in this equation than yours do.
He strings both of you along, has sex in two cities and doesn't pay alimony or child support (if applicable). Your own desperation is feeding this behavior. And every bit of this is feeding his ego. If he thought you wouldn't fight for him, he'd be wondering what he'd done wrong, and trying to fix things. He's got two women gaga over him. The mistress might not even know that you exist.
Call his bluff. Call a divorce lawyer (this does not mean you ever have to actually file). Tell your husband he doesn't get to live with you while this nonsense goes on.
Right now, this has been too cheap and easy for him. Turn it into two households that he has to support. And he'll see if his mistress ponies up to pay for your maintenance, or if she'll tolerate it if he's broke because he's getting a divorce and then paying alimony.
And maybe she will. And she can have him, yes? This is a lousy position to be in, and I feel for you, but if he is caught redhanded and is still harping on taking care of her feelings when you
are obviously hurt, then he is not putting your needs first.
You might want to rethink wanting to be married to this guy.