I think you've already received really sound advice so I don't have a lot to add. I think Anthro hit the nail on the head. The place to start is with the question he suggested you ask yourself. I think it is very important for any of us to know exactly WHY we are choosing to stay. But in your case, I think it would need to be a very powerful reason at this point with all that you have gone through.
The other point I'd like to make is that this is YOUR LIFE. Do not let anyone - family, friends, people on this site or any other - tell you how to live it. You have already had far too many choices made for you. If you want to stay with your husband and keep working on your marriage - DO IT and don't let a soul tell you differently. But if you are tired of DDs and are tired of working on your marriage - THAT IS 100% OKAY TOO. And don't let anyone make you feel bad about it. You have clearly tried everything to save this marriage. So if you decide you are done, you should leave with the cleanest of hearts. This was in NO WAY your doing. I am incredibly disappointed that there were people who made you feel that ANY part of this mess was your fault or that you weren't handling it "correctly". That is bullcrap. You have fought tooth and nail and FAR, FAR harder than most would. You have every reason to hold your head high. And if you choose to stay, it should be your husband doing intensive therapy - because that is where the problems are arising. While there are always things we can work to improve (to become a better spouse, parent - or overall human being) the only one repeatedly returning to dishonest behavior is your husband. He needs to figure out why. And that is something you can't do for him - or make him do. He has to want it for himself and for the people he loves. If not, you will always be waiting for the other shoe to drop.
BS - Female
Married 27 years, one adult child DD May 2016 “When we are no longer able to change a situation, we are challenged to change ourselves.” - V Frankl