You can't trust him no matter what he tells you. That's what it comes down to. No, they don't care if it hurts you. No, they don't care if it negatively impacts the children. They do what they want, when they want and with whom they want. That's all that matters to them.
Also, stop having sex with him. It's not helping your situation and you are exposing yourself to possibly catching an STD every time. I'm sorry if you don't like my Honesty, but to be fair I don't like your lies.
Sometimes it's better to push someone away...not because you stopped loving them but because you can't take the pain anymore.