Of course wanting your own time doesn't mean you don't want your kids OP. Personally, I believe that every single person needs time for themselves, but it sounds like you don't get any, other than when the kids are asleep, and even then you're not allowed to go out, because it would mean that your husband would have to care for them. This is WRONG on so many levels OP, can't you see that? I'm guessing by the title of your thread that you can't? As there is no way that YOU are the ARSEHOLE!!
Do you have any friends or family close by OP, or has he alienated them all?
Do you work? Or is he also happy to keep you at home so that you don't get any big ideas about leaving?
Other than the fact that HE IS ABUSING YOU, which you really NEED TO DO SOMETHING ABOUT, it is possible to lose weight and get fit, without going to the gym OP. Why do you feel you've gained weight? Do you snack because you're miserable, bored, etc?
Going out for a walk will help make you feel better, as well as burning some calories, and presumably there's nothing to stop you doing that, whether you are looking after one child or all three. What about gardening? If you have a garden, the warmer weather and light nights are fast approaching, get out and lose yourself in pottering in the garden, again, it burns calories, whilst giving you the boost of being out in nature and getting fresh air. Or, how about dancing? All the kids can do that with you, and even if you're not able to do much to start with, if you do it often enough you'll be surprised how you quickly you will gain energy and be able to dance for longer.
So, even if you don't feel you can tackle the abuse side of things yet, because he's drained you of your confidence, why not focus on losing weight, and getting fit, without the aid of the gym, and then, when you're feeling better about yourself, hopefully your confidence will grow, and you'll feel better about dumping this piece of crap that is doing his utmost to keep you down.