Well, you are entitled to feel however you feel about sex. And to never have sex again, if you don’t want to. You aren’t wrong to feel that way. It does sound like there is a lot going on in terms of your health, your caring responsibility and TBH your relationship doesn’t seem in the healthiest place- all of which could be contributing to your lack of libido. Or, perhaps, this is just how it is for you. Either way, you are entitled to your feelings and should never have sex if you don’t want to.
But, others feelings about sex- e.g. that it is very important to them within a relationship and something they don’t want to do without- is every bit as valid as your feelings. Your husband is not terrible or disgusting or a horrid person for wanting sex daily or multiple times a day, just as you aren’t any of those things for refusing sex.
However, this may mean you simply aren’t sexually compatible. Perhaps relationship counselling may help? There will often be strain on a marriage where sex drives and the importance placed on sex are highly divergent between the couple- especially if one partner unilaterally simply decides “nope, not for me. End of” or only agrees (begrudgingly) to keep their partner “happy”. It’s not a great feeling (been there) to think your partner is probably only agreeing out of a sense of duty. It’s pretty degrading, actually (and then, in turn, puts you off too). But then I guess feeling hounded (even if not the intent) for sex is pretty miserable too.
I think you need to seek counselling and talk it through. I’m not convinced that this relationship is making either of you happy- he appears to feel rejected and you feel pressured into having sex you don’t want and with a man you don’t seem to particularly like. You say you need him to stay because of your child. Do you actually want HIM, for him, or just because you need his physical help with your child and financial support too? Because I don’t think it’s fair to either of you to be trapped in an unhappy relationship for that reason.
I mean, it’s pretty grim to feel that your partner only wants you around because they need your financial support and help with your child, that they don’t really want to be in a relationship because they love you and who you are and that they don’t want to have sex when it’s important to you. And make it quite clear they they feel that the fact you want sex is somehow wrong. I know from your flip side things aren’t great either- ? Feeling he’s only interested in sex, doesn’t understand your point of view and so on (and his infidelity is a problem).
All that said, I wouldn’t want to stay in a relationship where I was tolerated as a “necessary evil” and sex was off the cards forever (or permitted rarely, under sufferance). In part, it comes across as though you want the marriage to continue for convenience/support without being overly fussed about your husband (I.e. he could be anyone who could fulfil the need for supporting you with your child and providing financially). If our husband picks up that vibe too, it must be quite tough. You can still co-parent without being married, and that is more likely if a split is amicable.
I think if left unaddressed you will both grow more resentful of each other and it won’t end well.
I have been in a similar position to your husband with an ex-partner whose libido had always been lower than mine but nose-dived after a while. He simply decided it wasn’t happening, made me feel guilty/that I was hounding him for even suggesting sex- so much do that I stopped even hinting or suggesting because he made me feel disgusting, or that I was being totally out of line/horrid and pressuring him. It was miserable- I felt rejected, unattractive, knocked my self-esteem, made me question whether I actually was behaving terribly/was I a bad person. It was not great. Until I realised that, actually, I wasn’t wrong for wanting sex or to ask for it (as long as fully respecting a rejection etc), just as my partner wasn’t wrong to not want sex. What wasn’t ok was a unilateral decision by my partner, with little discussion and no effort to look at my needs/wants either.
looking back, it felt like emotional manipulation to make me feel “wrong” so I would stay and ask no questions- I am not really sure why he wanted a relationship with me because it didn’t really seem to make him happy but I do sometimes wonder if “someone” was better than nobody. I think it is true that had he cared about me then he would have made an effort to try and address the issue in some way, together, instead of turning it into a “me” problem.
i left, and it was the right thing to do. We weren’t married and no children. Best thing I ever did. Maybe it will be for you both too? If that’s not what you want, then you need to work a healthier way through it and couples counselling could be a good place to start.