@GinPink I really feel for you. I don't have children (I am pg) but like you I was an 8-10 when my partner and I got together, and am a 12, sometimes a 14 now, which feels big. His last job was incredibly stressful, and during the time he was there he became basically sexless. Like the impulse wasn't there, like I was his sister or something. He'd never been that demonstrative, and I always had a mini anxiety that he didn't fancy me, although we did initially have a great sex life, and over time he became more cuddly and willing to hold hands, have a smooch etc. But at this point in our relationship it was like a light had gone out. I was afraid that he had an OW but actually I think he just didn't think about sex at all - and it totally tore me apart. It made me feel so unhappy and unlovable, compounded by the fact that I had gained weight - I didn't know if it was my fault. I tried to hide it most of the time, but he did know that I was very upset, and he felt guilty about it, but sort of interpreted that as him being a disappointment and not good enough etc, which made him retreat more into his shell. He'd ask me to please keep instigating, but from my perspective, 75% of the time I tentatively instigated, he didn't respond at all, and it left me feeling even more awful. When we did have sex, I felt so much pressure that I couldn't relax/get wet/orgasm, so he'd be all dejected and inadequate about that - I felt I was constantly managing his emotions as well as my own.
This is all quite painful to me still, and I haven't spoken to anybody about it really. But I am telling you because I hope it makes you feel a bit better. We spent about 18 months like this and I really thought that was it for our sex life, and was so miserable about it because I really, really wanted sex to be a part of my life - but I wanted him to be a part of it too. I don't know if I could have left him over it, because he is my One.
I think if your husband is getting hard, that's a really good thing. He is capable of being aroused around you. I've noticed that lots of men make jokes or glib comments rather than admit that they are the ones who feel inadequate, sexually speaking. He doesn't necessarily have this as a conscious thought process, but by being light-heartedly mean about your body, he's putting you on the back foot rather than him. It could be that he doesn't even think that what he's saying is bad, but when he does it he is desexualising you. OP, I really need to tell you that YOU ARE ENOUGH. The problem is not with you. Don't let him make you feel that, and don't make yourself feel that either - I know that disordered thoughts are very easy to give space to in a situation like this.
I think it is highly likely that he is a bit depressed, perhaps through circumstance. My partner and I have a pretty good sex life now - not like when we were first dating, but it's enthusiastic, mutually satisfying, and probably averages out to twice a week. A lot of the key to that was communication, really laying out for him how I felt, and being strong enough to hear him when he said what he felt, even if it was painful to me. I also had to accept that I would need to be patience - things were not going to get better at the flick of a switch; they took a long time.
I'm afraid (because this may be out of your control) that one thing that helped enormously is a change in circumstances - he has moved job and our living situation is quite different, and as his stress dissipated, his sex drive came back like magic. There is a lot in your situation that you can't change, and I agree that perhaps being at your stage in life with 3 littlies is just something you will have to wait out. This doesn't have to be forever ,although it may have to be for now, but you can communicate your way through that if you start thinking as a team. In the meantime, can you try doing little things that don't lead to full sex but are still enjoyable and erotic? Whatever gets you off. Take the pressure off both of you, and start showing one another that your bodies are enjoyable.
Sorry this was a bit of an essay. You just really touched me and I wanted you to know that it can get better. Leaving aside all the rest of my rambling, I think the very central thing to how you approach this is, tackle it as as a unit. Both of you together. Don't allow yourself to be isolated from him by this; don't cast yourself against one another when actually you should both be fighting for the same thing: the health of your relationship. Just do right by him as far as you can, and demand that he does right by you as far as /he/ can: you need to listen to one another, respect one another, see one another. It's too easy to drift apart when life gets in the way.
I wish you very very best of luck.