OP, it sounds like you have good insight but are a bit afraid of accepting the reality here. Sorry if that sounds harsh, I don't mean it to. I understand exactly where you're at.
Your husband is contributing a lot to this problem. So are you. Doing it to just do it is terrible for you (the anger, the aversion, the disgust is your body screaming at you to stop giving away your power). You have the right to say no, this isn't working, even if it has negative consequences for your relationship.
You say your husband doesn't pull his weight at home, is always at work, doesn't do anything to make you feel loved or valued.... Even in an asexual relationship, these would be problems. You mention he's not putting much effort in with your little one; that must make you furious! You've probably lost a tonne of respect for him. I would bet THIS is why you're so angry. You feel totally neglected by him, and resent him for turning into what sounds like a shoddy excuse for a partner and parent ...
You are giving too much of yourself.
Have you sat him down and told him "you need to do more, I feel unloved/neglected, and your daughter needs more than you're giving her"?
Another important question, which I'm not sure if you've mentioned. Imagine you could rewind 5 years, be single. You're happy and healthy. Do you have an active sexuality? Are a sexual person? The question I'm asking is, is there a part of you that would like to reclaim your sexuality for YOU (not to save your relationship)? This is a really important one to figure out. If no, then you owe it to your husband to inform him of that and work through the ramifications. If yes, then that's a great start and there's loads to explore.
To add, I have a whole load of empathy for your situation. I've been in a very similar place. I started going off sex for no real reason, though deep down I knew I had trauma I just wasn't dealing with. I'm not saying that's you. But I was also with my partner who I felt was emotionally distant, and didn't seem particularly interested in showing me love. I felt taken for granted and unloved. On top of the trauma, why would I want sex? But I did what you're doing, doing it anyway, it was awful. For a good three years, I could have told you and believed "I'd be happy never to have sex again". However, after some proper serious conversations with my partner about the state and dynamic of our relationship, and starting couples therapy so that my needs are met as well as his, we have so much more emotional and physical intimacy, and sex is no longer something that just has to be tolerated. When I don't want it, I say no. Always. I want to be sexual for me, and it's such a weight to be lifted. (It's complicated because of my trauma, so it's a slow journey but I'm getting there). So will you.
I must add, my partner never pestered. I couldn't stand that. He was always so respectful, he understands I'm not a sex-tap he can switch on whenever he feels like it. I asked for a 6 month sex break while I was doing my therapy and he understood and we made it work. He realises were in this for the long-term, and 6 months in a 10 year relationship, plus wherever we get to in the future, is worth it to build a safer and happier sexual and emotional life.
I'm not ruling out you may be on the asexual spectrum, but I think the way you feel treated by your partner - plus your own overriding of your rightful anger/upset at that by having sex anyway - is what's causing these feelings. And you owe it to yourself to resolve this stuff, regardless of the outcome in your relationship. I think you're angry at your H for a lot of reasons, but one because you want him to recognise you mean no when you say yes. That's not reasonable; there's only one person on this earth who can honour and listen to your intuition and that's you. You need to respect your inner voice, even when it's difficult!
I don't think this is about your weight, or hormones (though they may be exacerbating the situation). This is about putting your foot down in your relationship and asking for what you want and deserve: a mutually respectful and loving dynamic where you give your sexuality freely and happily because you feel loved, supported and cherished as a person, not as a mother and a sex-robot. And where you honour your own feelings, and stop having sex until you feel safer to have it, and say no when you mean no, even if your husband strops for 6 months, or goes off with someone else. His other option is to do the adult thing and work through this with you as a team. I'd arguing getting back to therapy could be really good for you.
I'm so sorry for what you're going through; I really understand how horrible this situation is, and I just hope any little bit of what I wrote might be helpful to you.