Infidelity Support Group
Any relationship in which one partner engages willfully in sexual relations with another outside of the partnership is considered to have experienced infidelity. This breach of trust is often traumatizing for the faithful partner as well as the relationship, and support is often needed to heal emotionally and to decide whether or not the relationship should continue after...

If he says he wants to stop, make him go to therapy. Or at least Sex Addicts Anonymous, which is a free group (you can Google it to find a location near you, or they have virtual meetings).
Cheaters lie. Cheating is a choice.
Do not put up with his infidelity. Put your foot down. If he can't or won't stop, then consult with a divorce attorney to protect yourself, your money, your assets.
By the way, what does he mean by "emotional relationships with other women"? Is he seeing these women in person? Buying them gifts (with your money)?
You are strong. Stand up for yourself.
I'm sorry about your first husband.
What do you want to do next? Are you fed up and ready for divorce? Please consult a divorce attorney so that you get everything you're entitled to. House, spousal support, half of his 401k.... don't want to leave anything out that you are fully entitled to.
In the meanwhile, please keep in mind that he can bring home HIV, STDs, and even get another woman pregnant. If he gets another woman pregnant, you will be on the hook to pay for half of their love child, since you two are married. They will take your salary into account. Do you want to pay for his illegitimate child with another woman for the next 18 years? Have him bring HIV into your house?
Sorry to be so blunt but you need to see the reality of the horrible things that he is inviting into YOUR life. He is choosing this behavior. If he won't go to counseling, I would file for legal separation. To protect your assets from these other women. He has no regard for you, then you have no regard for him. File for legal separation and tell him to move out.
Mentally “not right”and I said that’s not my problem and no excuse for his behavior.
You do not, and should not, put up with what he is doing. What he is doing affects you in so many bad ways.
If his therapist even said he is mentally not right, then he needs an inpatient program.
Be aware that some people will just announce they have a sex addiction, as an excuse to cheat without consequences.
Think about whether you really want to stay in this marriage or not. Think if this is how you want to live the rest of your life. Would your late husband want this kind of life for you.
I deserve better. And so do you!