The mentionitis of the woman at work, and telling the DC do seem to point to an OW...or the chance of making something happen by being 'single'. He wouldn't tell you at this point, he would be ashamed [you'd hope] and not wanting to take any blame. Sorry OP, I know how awful this is for you. I've been through it all myself, it stinks.
However keep your dignity, don't chase, beg, or contact apart from arrangements to do with the DC. At their ages though maybe dad and DC could arrange to meet up between them, leaving you out of the loop. It would be easier on you. Keep a distance, be cool, no arguing, persuading or chewing it all over with him. Be indifferent.
Take it one day at a time, look after yourself, eat well, rest, see friends, keep busy, walks, new hobby, distract and treat yourself. Do nice things with the DC, plan weekends, days out, a holiday, decorate one room at a time...make a new life.. There will be days when you want to be quiet, grieve, get your finances in order, feel sad...the next day will be different.
Feeling betrayed myself, I am letting go of someone capable of hurting another human so much by being underhand. The stages of loss are denial, anger, depression and acceptance...I'm now in between depression and acceptance. The person I once knew has gone. I really wish you and your DC's well OP, you are being strong and level headed. His loss.