Dear OP, I am so sorry for everything you are going through. I have also split up from a HNW husband, (well he was on the cusp of becoming one) - there is a real grieving process for the life you should have had where it not for the stupid acts of the ex. However, I am so much happier now.
But re the 2 parents for kids statement.. I really want you to think this through.
Kids pick up things, a disrespecting, absent father, token presents to mum, etc they will pick it up, they will see and compare their homelife to their friends. Money does not make a good family home. One day, even when they are adults and have their own family etc, they will find out and you may find your kids will get angry with you for staying and letting yourself be walked over (by the way you describe his reactions it is unlikely to be his last mistress/fling), or they get angry at their dad at his disrespect to you and them - the point is it will come out as he is not sorry and therefore he will not change.
You will be teaching your daughter by example, that is is OK for her to stay with a man who does not respect or love her, or a son, that is is OK for a man to treat his wife, mother of his children in this way and that the woman needs to put up with it..... There is so much more at stake here. Please get some counselling for yourself, talk to a solicitor and don't let your wishful thinking take over.
The reality is he broke the family unit, it will never ever go back to how it was, no matter how much he or you can pretend - things will never be the same again. If he was truly sorry, there may have been an opportunity for growth on his part and working together with counselling etc to make a new family unit based on honesty and transparency and hard work - but he hasn't in any way signalled this, so there can be no happy after, only sweeping things under the carpet for appearances and that will not lead to happiness for you or your kids - you deserve more ( no need to rush things, but do investigate the solicitor, counselling etc).