So sorry to read about your sad situation. For such a common problem in marriages, its amazing there is no obvious solution.
You wrote a very full account of your struggles, self improvements and love for your wife and children. You've obviously read all the books and professional advice and I know how hard it hits you when despite adhering to the advice, nothing changes.
You wouldn't be normal if you didn't feel the resentment that you describe. Unfortunately, that resentful bubbles over into other areas of the marriage, which is a shame as you describe your wife as a caring and conscious mother.
Every marriage goes through flat periods with physical intimacy especially as the marriage gets well into the second or third decade. It my experience it can be recovered to some extent but is unlikely to return to the lusty early courtship days (not that you said you were looking for that).
Your wife is being truthful with you at least the extent that she is no longer desirous of sex because she no longer has the urge. If you think about it logically, if she wanted to be physically intimate, she would. She doesn't so she doesn't. You can't persuade or push her into having sex, she wouldn't enjoy it and I suspect neither would you.
So where does that leave us. It's decision time. She refuses to go to therapy. If nothing changes you will become a broken, empty, angry man. You need to set up a conversation with your wife. Give her advance notice. Select a time when there will be no interruptions or rushing out the door. Tell her it's important. You need to explain to her that the lack of intimacy is not your problem or her problem - It's OUR problem.
Explain that you are dying slowly internally. The man she married is declining into a sad empty shell which she will no longer enjoy being married. Ask her again to attend appropriate counselling together. If she refuses, she needs to be shocked into seeing the reality of the situation.
That reality may involve ending the marriage. From your post I sense your wife doesn't see the gravity of how you are feeling. Ultimately, it's up to the two of you to make it work. If only person is making the changes, the marriage can't survive. That is a very sad outcome but your mental health is at stake here. Good luck.