I think it is a good thing you are seeking professional help for your marriage. How is that "being a doormat." A doormat would just sit home crying and not doing anything about her cheating husband. If your marriage is worth saving then you should at least try. If in the end it fails at least you have the knowledge that you did all you could to save it. You can walk away with your head held high.
As for your friend. Your the one in need a good friend would be there for you. It is up to her to be a support for you or not. Sounds to me like she has to much of her own baggage to deal with.