It isn't over until it's over. I'm currently dealing with a WAW myself. The biggest problem I see with your situation is that by the time she decided to start letting you know that she was unhappy, she was already going on dates. That's rough, man.
The good news is, if you can forgive her, it doesn't have to end there. The best thing that you can do is to keep it together and continue life for yourself.
However, I don't know where you all stand financially, I would get her brakes fixed if possible. If she gives you any grief about it, calmly tell her that if she is going to be driving your children around in that car it needs to be safe. Then drop it. Don't justify it any further, don't accuse her of not caring, etc. If she says anything about it, just respond as bare minimum as possible. The reason being is that you seem to be the mature one in the situation here, so you might as well be the responsible one: She shouldn't be driving your kids in a car with bad brakes and you are willing to put all the negative feelings and situations behind you for their sake.
In the meantime, keep up the faith-keep up the prayers. I'll keep you in mine, so drop one for me, if you don't mind.