Distracted OM pursued you because? what? what did your hubby do when he found out?
Many WAS say nothing will change and nothing might, but there is always hope. He is angry now. He doesn't want you back because you violated his trust. It is time to own up to your responsibility in this situation and repent like you have never repented in your life.
One letter will not do the trick. One conversation will not either. You have to be patient. And work your way back into his life. You have kids together? if so, you will have to prove to him that you are worth of his trust again and vice versa.
God I wish my wife was you right now. Wanting to come back to me. I would very much welcome her with open arms but even if that happens there is so much trust to be rebuilt. There is much work to be done.
You cannot give up once you attain what you want. And even if you don't attain it, you have to persevere.
Read divorce busting. Get a coach. Get a life
You can be a very valuable member in this forum simply because you are a WAW that came back. By helping others with walk away wives you might be able to find the answers you are looking for.