I do wish people would stop assuming that women generally don't want sex, but might magically warm up, if the husband does more "chores".
Some women have high sex drives, and are up for sex 24/7, regardless of who is doing the chores. I would have sex every day, if I could. I would even have sex with DH after an argument, if he was to take his clothes off and give me the come-on. And I do far more around the house.
Anyway....in a previous relationship, I behaved exactly as your wife is doing Op. I was having an affair. In my defense, this was after discovering that my Partner had had at least 10, whilst I had been faithful.
Your wife isn't going to dance class, or away for weekends with friends from the class. She's 100% seeing someone else. You need to get in to her phone/texts/whatsapp/facebook/e-mails etc. Trust me on this one. Because unless she's dead below the waist, she is getting sex from somewhere.
Did you have an affair in the past? Because this can be the catalyst for a woman to completely switch off.
After 4 years, why on earth haven't you given her an ultimatum? 4 years is a ridiculous amount of time to go without sex.
How old are you both?