Hello, I'd like to help you with your question.
It can be very painful when your spouse has a relationship outside of your marriage. It is common to feel disbelief, shock and devastation. It is a loss and grief is a normal reaction, which is sounds like you are experiencing.
Relationships that start while a person is still married very often do not work out because in order to do this, the person has to lie and also hurt someone they love. And that means something is wrong with what they are doing, not a great way to start a new relationship.
You mentioned that your husband is 66 years old while the person he is with is 29 years old. That is a big age difference. While some relationships can survive that much of an age gap, many do not. There are too many differences and the partners have a difficult time relating because of it.
While it is hard to tell why your husband has started this relationship with the young woman, many men stray outside of the marriage with younger women for a reason. Many times it can be because they need to feel younger. Aging often frightens people, and a knee jerk reaction is to try to recapture youth by being with someone young instead of dealing with how they feel. Also, men may feel it makes them look good in society and more virile to be with someone younger. Ego plays a large part in seeking out relationships with younger women. But these reasons are not good foundations for a solid and lasting relationship. They are often self centered and therefore not a good reason to have a relationship.
It's important that you do what you can to take care of yourself. You are in pain and the betrayal of infidelity can feel overwhelming. It's ok to grieve. Though it is difficult, you need to work through the pain. Be sure to get a lot of support during this time. If you do not have supportive family and friends, consider seeing a therapist. And even if you do, talking to a counselor can help you learn ways to cope. And try an on line or in person support group for more support. Also, learn as much as you can about infidelity and how you can help yourself through this. Here are some resources to get you started:
Surviving Infidelity: Making Decisions, Recovering from the Pain, 3rd Edition by Rona B. Subotnik and Gloria Harris
Transcending Post-infidelity Stress
Disorder (PISD): The Six Stages of Healing by Dennis C. Ortman
He Cheat on Me?: The Truth Behind Why Men Stray by Rona Subotnik
I hope this has helped you,