People should really stop giving the advice of changing locks in a jointly owned home.
You can't unless you have a court order excluding your spouse from the home, although you can change the locks on the marital home, you cannot prevent your ex- from returning to the home, even if that means breaking into the home, or even changing the locks again to lock you out.
I doubt he stopped using prostitutes at all. Stop worrying about proof of his behaviour...he's untrustworthy and violent.
Forgiving him has tied you to him for longer, as you had a third child in that time.
He doesn't respect you, but wants the status of being a married family man.
With his violence, don't rise to him or get into arguments. It won't get you anywhere, but deeply stressed out.
At this stage you need to focus on yourself and your children.
He needs to know you don't want the marriage to continue and supporting the DC through iylt all is your priority.
Don't let him be the focus... ppl like that are never wrong in their opinion.