I think this one is really difficult:
From your point of view, you aren't drinking a massive amount, and don't appear to have any type of problem with drink from what you say. You enjoy drinking once a week, which isn't endangering your health, wasting loads of family money or anything else, and you quite understandably feel somewhat controlled by your partner when he tries to stop you doing something you enjoy. (and it sounds like he has form for being low-key controlling about random stuff in general, which is no doubt adding to your frustration.)
From his point of view, being around a pissed person (even if only somewhat pissed) is often not a lot of fun when you are sober. I used to have a drink problem and am long-term sober now and I have to say that I cannot think of ANYONE I know whose personality is actively improved by drinking. And in my experience it's those closest to us that become the most annoying when drunk - I have absolutely no problem being around random acquaintances who are drunk; with some close friends and family it frustrates me a bit after a while ; and my (completely wonderful) husband, when he still drank, used to annoy me ENORMOUSLY when drunk (tho I accepted of course that it was his free choice to drink) - he repeated himself, insisted he was right about random stuff, was much more quixotic and moody, and just generally not nearly as interesting or fun to talk to!
I have no idea if you are like this to any extent OP, but if you are I can feel your husband's pain! No judgement here at all from me towards people who drink - how could there be? - I was the worst drunk in the world before I stopped! My husband (who is a fucking MARVELLOUS human being) eventually decided to stop drinking himself after I had a lapse and fell off the wagon during a rocky patch, and he decided with the help of a counsellor that he could better support me in my sobriety by going sober himself. It's been brilliant for both of us and I am SO lucky to have a man who has done this for me - I know it is not something anyone ever has the right to expect or demand.....
Your situation is different and in a sense less pressing. So I was wondering if a compromise was possible - could you have a night out once a week and drink then, if he is happy to stay home with the kids? Either out with a friend or, if money is an issue, go to a friend or family member's place if you have any close by who like an occasional drink too, and share a bottle of wine and a chat? That way, you still get your chance to enjoy a drink and unwind, but he doesn't have to get frustrated by you if you are less than brilliant company when drunk..... Reciprocally, he should also get a night out once a week seeing a mate or doing a hobby or whatever, if he would enjoy that....
Sorry, that is an epic response - hope none of it sounds offensive or judgemental, because it really isn't meant to - I see everyone's point in this situation!