Betty, I think that actually a bit of intimacy (and I'm not necessarily meaning just sex here), will actually make you feel happier in the relationship anyway.
Its a viscious circle though, because if you're anything like me, its hard to be affectionate when you don't feel loved and cherished back, and his ultimatum isn't exactly helping!
Do you have parents around, or someone that you can trust to have your child for the weekend, and you and your husband can maybe go away for the weekend. It'll give you a chance to prioritise on eachother, and there may be sex, there may not, but it gives you the chance to see eachother as lovers, and partners, not just the mum and dad that you seem to have become. If money is an issue, sometimes you can find bargains on Airbnb, or even if its just a travelodge, but just spend some time together. Make sure its for 2 nights, not just 1 though, so you can catch up on sleep the first night!
Obviously he needs to realise that he doesn't get a weekend of undivided time as a reward for being a dick, but if things have reached crisis point, then you probably need that time together.
As part of spending time together, you can work out together how you can fit some coupley time in your lives. Not sex at the moment - feeling coupley and loved will lead to you wanting more sex, but you are wanting to get the connection back between you first.