Try your best to ignore his mother, just put her comments out of your head because they are total bullshit. Your EXH is a bastard who has lied to you and has the gall to bully you when he is the one who wrecked your marriage and upset his own children . I get it that marriages break down, mine did, but his behaviour is abysmal.
You haven't done anything wrong. I would contact his HR department and ask if they have a policy on relationships amongst staff. I work for a very large organisation and this is not an uncommon question. If they do have a policy, ask for a copy of the policy. You never know when it might come in handy.
I am not one bit surprised that you have lost your perspective on things you have been through a dreadful shock. It is scary and lonely at the beginning and you just have to accept that, there would be something wrong with you if you didn't feel those emotions. If you need to see your doctor or a counsellor do so. Focus on yourself and getting yourself better.
Be 100% honest with your children, you don't need to slag him off, just tell the DC what happened. Don't worry about being 40 and single. You have your whole life ahead of you and allow yourself to be a little bit excited about that prospect. You don't know what is ahead but is can be so great. You will meet someone when you are ready, don't rush it now, just be kind to yourself.
Your EXH and his bit on the side might think that everything is rosy, just wait until reality sinks in. See a solicitor as soon as possible and sue him for divorce on the grounds of infidelity. Get advice from your solicitor on how to protect yourself financially. Other MNs will have advice in this regard.
The reality of what is ahead for him will soon cool his ardour. She is really going to love it when the excitement of their secret trysts is over and all she is left with is a bullying liar. She will never be able to trust him, she has seen what a brilliant liar he has been for the last four years. Good luck to them you are well rid!
Stay on top of your job, you are doing brilliantly!!!!