It will only work, for him and for you and for the children, if he is treating WFH as if he is actually at work. I WFH and have done for a long time. I have an office room in our house. When I go into my office and shut the door, the rest of the household knows I am at work and they can text me if they need something urgently but nobody comes in and I don't go out apart from loo visits. There is no need for anyone else in the house to be quiet, because I use headphones if I need to have a meeting or something - and if any noise is preventing me from concentrating I can put the headphones on and have quiet music instead.
I have a tiny fridge and a kettle in my office and when I go up to work, I take eg cheese, salad, bread, butter, store the things that need it in the fridge and make my lunch as if I were out of the house. I might occasionally do myself an egg on toast downstairs or heat soup, but mostly I go into my office when I start work and only leave when I have finished. Then I shut the door on work and am completely done with it. The benefit of this is not only that the rest of the house is our home for the other people in it, but also that I can shut the door on work and it doesn't spill over into my own home life.
DH works weird hours so is often around when I am working but it's fine. He doesn't bother me and I don't interfere with whatever he is doing. He might occasionally text me eg to ask if I want anything from Sainsbury's or I might text him and ask if he could record X on telly or something, but I expect we'd do that if I was working elsewhere too.
In your shoes, I think I would be telling your husband that this can only work if he uses the garden office and doesn't come out of it during the working day apart from maybe lunchtime (though, as I say, there are ways round this and he can perfectly well have a kettle, fridge and microwave in there - just like he would if he was in an actual office).
Also, stop tiptoeing around trying not to make noise. Buy him a good pair of headphones and explain to him that if the house is too noisy to work in he shouldn't be working in it.