First, congrats on 20 years of marriage. I understand that it's been very difficult at times, but you've survived. You've stuck it out. It sounds like your marriage could be turned around if you can put the puzzle pieces together.
I do wonder if the NFP is an issue. Worrying about getting PG is a huge libido buster for women. You mentioned that she isn't on board with NFP. Would she prefer another method of B/C? Is that an option for you?
At her (40-something) age, she's nearing the end of her child-bearing years and this can be a difficult time for many women. She may feel sad about that, even while at the same time feeling overwhelmed caring for the kids all day. As the mother of one child, I feel enormous admiration and respect for your W! Does she talk about things or does she tend to keep it all inside?
Do you thank her for caring for the children? Do you tell her how much you appreciate all she does? One of the most difficult things about being a SAHM (for me) was that it often seemed like a thankless job. Even if she doesn't thank you, try thanking her. When I started thanking my H he was surprised at first, but then I think he appreciated hearing it. Surprisingly, I felt good saying the words! Praise didn't come easily to me, but, being grateful for what I have really changed the way I see things.
It's good that you and your W go out alone once a week. Surprising her by taking her riding is a great idea. What other interests does she have? She's been in caretaker mode for so long that it probably doesn't even occur to her to do anything for herself. She may have forgotten what she likes.
Also, I think MrsNOP's ideas are great. I agree that you should tell your W how you feel, and that doing it in writing might be best. Your posts to Cemar demonstrate that you truly understand and I think that really gives you an advantage.