So he has a track record of adultery, a track record of deceit and lies, and a track record of walking away from his own child. So for four years he was shagging someone else and not only did he have such little respect and regard for you to do that in the first place, he even tried to force you to be friends with this woman. That's not the actions of just some sad, seedy and pathetic bloke who can't keep his dick in his pants. That's the kind of thing someone with a narcissistic or sociopathic personality disorder would do.
And it's only now, after he's been found out, that suddenly he's apparently so full of remorse. Well, some remorse, anyway, although I note he's trying to pin a lot of the blame on her as "she threatened to tell you". Oh how noble of him to carry on shagging her solely to prevent you being hurt by her telling you
He lied for so long and so convincingly about his affair. How can you possibly believe a single word that comes out of his mouth now? Do you not deserve to have someone treat you better than this? After all, they'd have to try really hard to treat you any worse.
I'm sorry your husband is such an untrustworthy, lying, emotionally damaged arse-wipe of a man. And I'm sorry that your relationship with him is so fundamentally broken. It's not your fault and you're having to deal with the consequences. That downright sucks. But if you stick with him through this, what you will be teaching him is that he can lie to your face, shag around as much as he likes, and then do the "boo-hoo, I'm so upset" act and get away with it.
Tell your friends. Tell this other woman's husband. Tell your family. The only person who benefits from you keeping this quiet is your unfaithful, unworthy husband. And, frankly, he doesn't deserve to have you covering for his sordid lies.
(Oh, and after you do finally kick this disordered twunt to the kerb, I'd recommend you get some counselling to help you make sure you don't pick another dud next time)