Hi, I'd like to help you with your problem.
From what you said, it sounds as if you and this man have had feelings for each other for a number of years and although you can now acknowledge your feelings and act on them, he cannot due to still being in a relationship that includes children.
You have a few choices here. You can continue the relationship as it is. This will give you a chance to be with him, however, you will always be on the fringes of his life and be second to his family.
Two, you can stop the relationship and end all contact. This would be the hardest choice, but it would also give you the chance to move on and heal.
Three, you can talk with him about getting a divorce and being with you. However, it sounds as if this is not a choice he is willing to entertain since he has children involved. But it would bring the issue out into the open and the two of you can discuss if it is a possibility. However, beware if he continues to put you off or says he will discuss it at sometime in the future. This is usually a sign that he does not want to divorce now, or maybe ever.
The main problem here is that you are not benefiting from a real relationship with him. He is dividing his time between you and his family, giving him the security of keeping his family intact, yet he can also keep his relationship with you. He is essentially getting the best of both worlds and you are not benefiting at all. It is up to you to decide if this is enough for you.
It would benefit you to seek out counseling with this issue. Not only can a counselor help you with your decision, but you can get the support you will need no matter what you decide.
There is a book I'd like to recommend for you as well. It's called "Will He Really Leave Her For Me?: Understanding Your Situation, Making Decisions for Your Happiness" by Rona Subotnik. You can find it on Amazon.com or your local library may have a copy for you.
I hope this answer has helped you,