Yes, we have discussed the chores thing numerous times. At one point the both of us attended my therapist in which this was addressed. Nothing changes.
The underlying issue at hand with him is that I am not fulfilling his needs sexually and this in turn makes him resent me. He thinks that if I would just give him sex things would change. But like I said, I can't bring myself to do this. I need to feel loved and respected in order to have sex with him and I am just not getting it.
Can you sit with him one more time and calmly work this out? But this time be armed with knowledge. For men, sex is their way of connecting emotionally with the woman they love. So his anger goes very deep, he thinks you don't love him and that he not attractive to you as a man, it effects how he feel in every aspect of his life. Did you know about the emotional toll lack of sex with the one he has chosen to spend his life with means emotionally to a man?
I am not saying that you are at fault or that you should have sex with him before working things out. But you are at an impasse now, your core needs are not being met and neither are his. He is wrong to not help you because you do not have sex but he is not thinking clearly because he does not feel loved or important in the family probably.
So about the sitting down with him. Start out by saying that you both have pent up anger and you think that the relationship is worth saving and would he be willing to work on it with you. Before you sit with him, read some books so you understand him and yourself better, you would be surprised at the reasons for his actions and you amy be able to see him in a more sympathetic light. Two books come to mind "His needs, Her needs" don't know author but Google it and "the five love languages" by G Chapman
After you read it then talk to him and tell him you have been working to understand where the relationship has gone wrong ask him if he would like to read the books you read. He has to understand that sex is not the problem, it is a symptom, you can't have sex and hope things will magically clear up. You have to both be committed to getting on the right tract and sex will come naturally.
Explain to him that you simply cannot have sex with him in order to get him to help you that he is treating you like a paid worker. Explain that you do not feel emotionally connected to him because of the things that he is doing. He does not feel emotionally connected to you because you don't have sex. Someone has to blink though to start the ball rolling. If you talk about it first maybe you can tell him that you will try to get more emotionally connected with him but you need for him to do certain things first.
Be very explicit about what you want him to do. The idea is that chores have nothing to do with sex and intimacy. The household and child care is the responsibility of both people. When he is not doing as he should you lose respect for him. You both live in the house and you both have children and you both work. It is only fare that the place where you both live should be cared for by both of you.
So you both feel the same way, sad, angry, disappointed, unloved, unappreciated. Remember the man you feel in love with he is still there, with faults but his essence is the part of him you feel in love with not because his was perfect. So you should both be sympathetic to each other and work this out.
All of the problems must be discussed not just the sex.