Definitely sympathize, you are not alone. I have a wife and two young kids. I love her but for a long time my wife just did not consider me as "at work" when I was working remotely. She had zero qualms about coming into our home office to chat or see if I could change a diaper or whatever. I'm happy to help out if I'm between tasks (hell that's one of the perks of WFH, and everyone takes breaks wherever you're working. I'm taking one to write this post!) but it was all day every day and driving me up the wall. Plus toddlers don't care about work hours, if they want to see daddy they're going to come see daddy. We had plenty of conversations about how disruptive it is to have someone tap you on the shoulder while coding to ask if you can run to the grocery store for milk. But it never went anywhere. To her, if I was physically in the house, I was available to do stuff at any time.

To be honest we never "solved" it. Eventually the younger reached kindergarten age and my wife returned to full time work. I wish I had better advice. The suggestion to have a dedicated office space with a door is a good one, but if your partner does not respect boundaries that won't be enough. If finances allow, you could look at leasing a part time desk in a coworking space or even a dedicated office. I know it feels silly to pay for office space when you can do the job from home, but if it's damaging your relationship, it may be worthwhile. Some employers might even offer a stipend for remote workers to help offset costs. The fact that you refer to your partner as a nagging micromanager tells me something has to change.

I hope this post doesn't make me sound like a dick. I have immense respect for my wife for choosing to pause her career to care for our children. Raising kids is HARD, harder than the work I get paid for to be honest. We're partners in life and parenthood. But my role in the partnership at that time was to hold down a job and that's a lot harder to do when you're being interrupted 10 times a day. Hope you are able to work something out.