A complicated mess

If you want my advice mate, and you can only act on any advice you get from here, because non us know the people we are talking about, only you know if there is a chance.
If you think not, you need to go to CAB,make some appointments with solicitors, see if you can get legal aid etc.
I would drop her a petition for divorce on adultery, if you dont, she will divorce you on grounds of UB, honest, she will.
You need to start to get her on her own feet but taking the kids into account oo. Whilst you are under the same roof, financially you will be better of. You will not need to pay her anything ike CM etc, you pay for the house so that is how it is for now. If you have to move out then it would be slightly different as she will need to either work or claim benefits and you pay CM, everything else is decided between you, in mediation or court.

You will find this is now a game and you cannot just shrug your shoulders and carry on, it will kill you as a person for your future. You need to think about yourself, your kids and make plans, you need o take control and put your best foot forward,.

I consider it aint that easy to get a partner these days let alone one that will take on an estranged wife with kids and a potential looming angry husband, so a) thats why i say it aint necessarily going to work and b) when the sex has died down what else is there with this other person? in this situation.

I couldn't agree more with Bobbinalong. She has you as a safety net and come back to you if things go wrong with whoever she is with. Furthermore, the reason she can do this, go out and have fun, is that you are there paying the bills.

Why should you fund her while she goes out and screws someone else? You need to think about you and the kids.

Get that divorce ball rolling. Don't allow here to disrespect you like this.