OP I'm reading your thread and sending support to you.
I agree with PPs views that your H has tried to push you into a sex life you didn't want, got pissed off at your (totally understandable) resistance and gone outside the marriage for sex, with prostituted women. He persuaded you that this was worth a try. Part of this deal was that you stay inside the marriage.
For a wife this would often be a divorce situation, but he's convinced you otherwise, because he wants all his money. He doesn't want to share it with you or the DC. He is, he thinks, totally entitled to cheat on you, limit your life choices and then keep you trapped so that he doesn't lose ££.
I am so hoping that you begin to see what everyone is meaning. You owe him no apology. You need to get away from him.
What I came on to say was my sons were aged 12 and 13 when they began to refuse to see their father 15 months ago.
He's furious with me.
He sent the Police, they came round spoke with me and checked on the boys, found no reason that the situation should change.
He has threatened some mysterious court action. Nothing has materialised.
It makes him crazed that he has to pay maintenance when he doesn't see them. He sees our children as his possessions.
I know that no court would be inclined to ignore the wishes of these smart SEN (and psychologically damaged) young people and their loving sensible mum, I choose not to worry about it.
Your DD is 15. It's over for him, he can "insist" on nothing. He can't dictate anything any more. You and your DC can be free.