Google "studio shed". $12K and your problem is solved.

OP here. Yes, I have a dedicated office space and I do keep my door shut. Thanks! The nanny takes them out somewhat but there is still just definitely time when they are here. It's just hard not to get distracted whenever there is some commotion going on. Pandora is a great idea.

I work from home twice a week. I either sit at the dining room table or in the office. The nanny takes the toddler out of the house almost all day, every day. If they're home, and I'm home, they're in the toddler's bedroom. If I'm not on a call I have earbuds in and Pandora going.

You need a separate office space (or else a room with a door, where you work and they don't go). Treat it like the kids are at daycare: all bottles, meals, etc. made beforehand or the responsibility of the nanny. Set defined break times when you will see the kids, and otherwise they're not to bother you unless there's an emergency. Trust the nanny to deal with their difficulties, that's her job. And encourage her to take them outside, it's nice out.

Good luck!

I'm now working from home, with a nanny keeping my youngest and my older one in preschool. I'd love some advice on how you worked best and made the most of your situation. Right now I'm having some trouble focusing, and it's hard to hear my nanny struggle with my two (very difficult) children.