You need help.
You need to find out how soon you can get into counselling. If you have to go on a waiting list for NHS counselling can you get some through work, or can you afford private?
Seems to me there are several issues here but they boil down to the fact that this man was never really available to you yet up to now there was always that slight chance that you and he would ride off into the sunset, together forever if only you could discover the magic formula and tame him, or if he somehow fell on his head and came to his senses. That ship has now sailed and you are coming apart because the dream is over.
Are you a person who prefers a dream over reality?
Will you be able to rally and start seeing yourself as much more than a has-been? What would it take to help you see yourself in a more positive light? The fact that she is 13 years younger than him and has no children and that he has been gallivanting around the globe for years says nothing about you at all.
Other issues regarding the children:
The material things being lavished on the children right now will not matter in the long run unless you turn this into some sort of issue. Keep on being mum, keep on providing what you have been providing for them, and do not doubt yourself or start looking at the children as if they are fickle beings whose heads could be turned by stuff. They love you and they need you -- but they need you whole and healthy; the only person who will be poisoned by the turmoil and fury you are now feeling is you and that will in turn hurt them.
They need to you to be there for them so they can deal with what is now happening in your ex's life, and you need help moving on/ examining why you did not accept any finality to the relationship's end so that you can be there for them, as well as being much more at peace within yourself.
They will find it hard to talk to you about all of this if you are in a heap or if you show them how much all of this is affecting you. You must not put them in a position where they feel they have to choose between him and the new woman in his life, and you. No matter how much effort it takes, you need to swallow hard and put on a neutral face for them, make it clear to them that you are there for them, and do not wear your heart on your sleeve. Do not dwell on the unfairness of this either -- seek help for your own issues and be determined to get through this and you will succeed.
I highly recommend the two of you find a mediator to help you both come to an agreement about visitation of the children and communication regarding events / developments in their lives. I recommend you get a schedule established so that the children know where they stand. You can bring up the issue of the GF at mediation but if they are living together or intending to marry and the children are not small children, then the question of whether it's too soon for them to spend time with her is probably irrelevant. Sucks but it is what it is. For his part, he will need to resolve to never again threaten to play your DS against you as he did wrt the match. This can be brought up in mediation and I do not think there is any mediator who would accept that there was any justification for that sort of behaviour. Family Mediators Association
Obv you are now going to go through the divorce process so you will need a solicitor. The mediation could form part of the wrapping up of the marriage (a lot of divorce courts farm out visitation and custody and child support discussions to mediators anyway).
You made a really good decision in going to the doctor's and I hope you will get some sleep and feel calmer. Going forward, you can start dealing with the grief of losing the dream of this relationship but you will probably need help getting through that.
xxxxx
I know this is really hard.