Irregardless of whether or not the church recognizes your M, it comes down to you.
You want out, then D. Period.
It seems like you're looking at all this theological stuff to justify what you feel. When it comes down to it, if hypothetically, the church (any church) says you may not divorce, you're going to want to anyway because you've never detached from your W and are feeling anger/resentment at her.
If you feel like you need to not deal with her anymore, then go ahead and file. Simple as that.
The main thing you should be concentrating on for long term, is how to cope with and get rid of the resentment and anger you have for her for the sake of the girls. That hasn't changed since day one. You call her money hungry, a lousy mom, etc. which you are going to have to let go. You may not think it comes across when you're with the girls, but I bet it does. Kids aren't stupid. They know what's going on. Even my 3 year old can tell when my W and I are upset at each other.
It's not going to go away after you D because you will FOREVER be bonded to her because of the girls. In fact it will get worse, especially once you see her with another man at your D's functions. Have you thought about getting help with that?
M-43 W-40 2D - 9 and 5
Emotion, yet peace. Ignorance, yet knowledge. Passion, yet serenity. Chaos, yet harmony. Death, yet a new life.