I haven't read previous posts, but the first thing that comes to my mind is how many of us women find ourselves in the same situation, or a variation of it, after getting married and having children. You just want advise all young girls in the world "Don't do it!!", sometimes.
Whether we work outside the house or not, we end up doing all the nitty gritty stuff around the house, and child care related jobs.
I don't have any definite answers, as I see it over and over again. I still don't think it is any easier for SATH mums either, as the pressure can be badly felt if you're dependent financially on your DH, plus not building up on your working experience is a tough sacrifice too.
In my particular case, things have improved since the children are a bit older as many men seem to enjoy more older children, and they get more involved in their activities when the children are older. But I have to ask and have argued a lot over the years, and I'm tired of the arguments too. But I do argue, because if I don't, the anger stays inside and can come in other unpredictable ways.
My humble advice would be to try to keep talking to your husband, until what you're asking settles in and he begins to understand a bit where you are coming from.
Also, be very specific about your requests, e.g "I want you to pick up your clothes when you finish with the toilet", rather than asking for help generally: e.g "I want to you to help more around the house".
Cannot he do the shopping himself? In my house, one of my DH's regular duties is to do a big shopping on Saturday, and then I buy bits and pieces as we go along through the week. He seems to enjoy going grocery shopping too, which helps.