A wise woman once said "fuck this shit" and she lived happily ever after.
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.
If someone keeps stabbing you in the back, then quit handing them the knife.