I gotcha. I am a mother to small children and I know how it is when they don't sleep and you are their sole caretaker. You have lost yourself. You need to find some childcare assistance for your own sanity. What about a high school kid who can help after school for a couple of hours even if all you do is take a nap or a bath? What about forming a childcare co-op with a few neighbor ladies? Right now I am not talking about sex. I am more concerned that you allow yourself some very basic breathing space.
About the toys. I can't say they do much for me either - maybe on a once in a while basis. To me that lacks passion, spontaneity, the human touch if it is all the time. I doubt it is because the only thing he feels for you is sexual desire but rather he may be hung up on only having sex with a "dirty" girl and when you use toys he is better able to get into the right frame of mind. IOW -he may have a few hangups (most people have some).
Are there some very basic agreements that you can reach? Can you agree to once a week sex in exchange for a once a week break from the kids?