You'll become a broken person if you stay with a husband who openly declares his love for another woman.
The truth is, he doesn't love her, or he'd be with her. He would not keep her as a dirty little secret.
He doesn't love you either, or he wouldn't do this.
He loves himself above any and everyone.
He wouldn't risk loosing you or seeing his kids everyday, or the safety and security of having two parents together if he loved them enough either.
Above anyone else, he loves himself and will cake eat just as long as you let him.
How many second chances does he expect you to give, without losing your self or losing any respect for him.
Get him to move out and give you space, otherwise accept your DH loves another woman and carry on as you are, quietly accept it and he'll probably wait for the kids to get older and leave you in years to come.
You'll have wasted time and find it harder to move on then. Meanwhile he'll have THE OW, if she's still stupid enough to hang on.. Many actually occupy the position of OW for over 10 years.
Your destiny is in your hands.