I currently work PT (3 days/week) from home, and go into the office PT (2 days/week) in MN. I will be having a third child and put in a request to work 100% remotely. I work in an office that many people work part time or full time remotely, so this is common. My director does not have an issue with this, because my productivity and efficiency in my work has not decreased when I work at home, it actually increases. However, our HR manager has an issue with people working from home for the reason of children (although many people already do that). I have not (nor has my director) voiced to him that the reason is my children, but I'm sure he concluded to it since I am pregnant.

Is he legally allowed to ask me if staying home with my children is the reason I want to work fully remote? Is he legally allowed to say that I must put my children in childcare in order to work fully remote?

First... Are you a Union employee? WHat state? If you are effectively an AT-WILL employee they can make certain demands including that you actually work from the office if they aren't satisfied the workspace at home doesn't fit their requirements. THey can even inspect your work area... and yes they can expect your full attention while you are being paid... and that means having someone else watch your kids while on th ejob.

If you are an AT-WILL employee... they can decide to reduce your hours or terminate you for any reason they feel like... so please tread carefully.

He can ask if you feel caring for another child, especially a new born will interfere with your productivity. You can answer that working from home has not reduced your productivity in the past and you are sure it won't in the future.