So sorry for you, OP. This must be awful. He IS lying to you; he says he has no feelings for her yet texted the OW, months after the relationship ended, to tell her that he missed her. You have the truth right there. He is disrespectful to you and your marriage and he's a cheat. Try to put the OW out of your mind, she's irrelevant and to give her words or thoughts credence is to make her of importance to your marriage - she isn't relevant, it's between you and your husband.
It might be the hardest thing for you to realise the truth, OP, but it's the truth that will set you free.
In your position, I think I'd want him to stay at his parents' home whilst I gathered my thoughts and decided what I wanted to do about the relationship. It doesn't matter what he wants, your relationship with him is not foremost on his mind, is it? Cheeky bastard... it's not even the first time. So angry for you. 
Do all you can to safeguard you, your children and even more importantly, OP, your sense of worth. His endorsement of you means absolutely n-o-t-h-i-n-g and having see you in pieces when you first found out, to do it to you again shows that he has no respect for you whatsoever.
Don't be lonely, OP, there are many people here who have been through this and similar and can give you great advice.