I thought maybe this was a problem with sex that has spread outside of the bedroom but I really can't tell. You have a host of issues and your wife sounds like an utterly selfish and lazy person. Which came first? The sex or the lack of effort in everything else? This is actually very important to the root of the issue. Problems with sex can destroy everything else, but if the other problems were there first then sex is probably just a symptom. Its a symptom either way but it has a more prominent role in the first istuation.
First, do not have sex with her. AT all. Just stop sexual activity until you guys get your relationship back on track. If you can't fix things, separate, but do not keep being intimate with this woman. She is very averse to sex. That is incredibly obvious and if she continues to have sex she doesn't want, your marriage will become even more toxic no matter what you do. Don't threaten divorce then take sex she offers. That is the worst thing you can do and it will doom the relationship for good. If you want to save the marriage, threatening divorce to get her to change won't work. It wil be a superficial improvement that will slip back worse than it was before. Sex is something people can not do because their partners want it. It just doesn't work like that.
You need to have a talk with your wife. Tell her sex is off the table completely until you guys resolve your issue. Be very clear that there will either be some open, honest discussion, or you will have no choic but to look at divorce. Again, do not take sex on offer after a divorce discussion. She will just be doing it because you threatened to leave. You really don't want that kind of sex. Trust me. If she has sex to appease you whle she doesn't want it, she will grow to hate you. Thats why I asked whether the sex or the other issues came first.
I'm a man in my thirties and I didn't understand how badly unwanted sex can destroy a relationship when I was younger. I looked at it as 'its sex. its fun. why wouldn't she want it.' and did not realize how badly I was ruining my marriage by coaxing and cajoling and whining to keep having sex even though there were a lot of other issues. out of all the problems we had, the sexual aspect took the longest time to fix by a wide margin. If you want to save your marriage, you have to stop any sexual activity. then get her on board with working on things together. Don't put sex back on the table until you guys have made some legitimate progress for a while in the relationship as a whole.