I can see your kids are pretty young. Yes, the sahm life does involve being with your kids 24/7. Your profile says you work part time? Do you attempt to WFH with 3 kids home?? Or are you working on days when your hubby is off work? When I worked part time, work was my break from the kids 😅😅 I think your expectations are unrealistic if you think you're going to home school but not have your kid home. I've not heard of a "home education drop off", that sounds like a fancy word for "a school". Fundamentally you need breaks and time off. Did you move closer to family or away from family? If no family, your partner needs to support you in having breaks.
If you want to keep the kids in the home can you get help at home? Not sure what your financial situation is but I’m sure having a nanny that’s on the same page as you or perhaps even someone to clean the house and do some cooking would be a big help? I saw you’re in London I’m surprised there aren’t good homeschool / Montessori options nearby, can you try looking a bit further afield? My SIL was driving 40 mins to take her son to a nursery like that
Maybe a private school your kid might just be shy from never meeting other kids