Look, this problem seems to have stemmed because you stayed in an unhappy marriage “for the children” and waited until they were in college to make your plans to leave.
You have prioritised you’re children & made their reactions/opinions/feelings the centre of your world to the point of martyring yourself in an unhappy marriage, so they could have the perfect mother part player for them
The problem is they have left the nest & you’ve crumbled without them. You had the chance to make quiet, well planned steps to leave but instead you’ve had an emotional meltdown & had an adulterous relationship, blowing up the family your children grew up their whole lives believing was real.
While almost undoubtedly the children would have learnt to Cope with a divorce & new partners in their youth, at this adult age it can be difficult to process, it must feel a bit like a death to them perhaps ?
I do not blame them for not wanting to know this man.
But i will say perhaps it’s time to talk to your kids like adults & tell them that you made a terrible mistake to stay so long and at the time you thought it was for them but in reality you were just scared.
You’ve made mistakes. You are human. You deserve love & while it may not have been done in the best way, what’s done is done. Live for you, if your kids don’t want to be involved, respect that. You waited so long to live for you while they grew up - they should not be at the centre of all your life decisions. They don’t need to approve of or understand every choice you make.
Own your decisions, speak candidly & that is the best way forward out of this I feel.