J.S.
I wouldn't be using sex as a reward or punishment. You need to have a healthy sex life within your marriage. Have sex on the nights you don't work or the mornings of. Make it work for you.
I think you need to sit down with your husband after the kids are in bed and tell him point blank that you need his help. That you need to feel that you both are a team. What you absolutely need him to do when you are at work - will a list help him accomplish those things? That if you know those things are done, you can actually relax. Relaxing being central to the sex being good.
Don't sweat the small stuff. Is it so bad that you put away his bag? He might appreciate it.
We all have felt unappreciated and taken advantage of at one point or another. You need to talk to your husband until he "gets" it.
Good luck.