Friends have done it several times and one friend's older kids have been in 2 different states for school. It is stressful but I will say that the DC area offers a lot for families. You may want to consider living in either Northern VA or Montgomery County MD, to be close to the city but not in it. If you like open spaces, be sure to get to Great Falls, and you can camp various places, including Little Bennet, up past Germantown. You might want to check out the local park and rec website for your chosen location. Traffic can be a pain in the butt, BUT if you are working from home, you will likely be able to avoid rush hour. Get past the city itself and I think you will be happier.
ETA: I agree to rent the house. Friends did that when they were away for a year, with the understanding from the tenants that they would need the house back in x timeframe. It worked out well, as the renters were doing a remodel and didn't want to live there with kids.
Obviously what works for one person may not work for another, but we live in the MD suburbs and both DH and I commuted via Metro into or through DC. I avoid driving in DC. I prefer Metro. The commutes will be long, just accept that if you are not in DC itself, but it was more like an hour vs 2. Rents and other cost of living will be higher than perhaps you are used to, but your DH has been here and knows that. My DH fills up out of town on his way home for a few cents off per gallon. Little things. I personally have not had major problems with the schools in our county. We have one student in college and one graduate and one in public school now. But they are not DC schools and I can't speak for those.
I would try to find out ballpark what the utilities would be for the house before you rent it. Our bills are not $1000 month and weren't even close to that before we got solar and insulated. It will be hot, and not a dry heat, so you will likely need to have the air conditioning running most of the summer and should factor that in.
I'm sorry Momof 1 has had such a miserable time, but I hope you can find the middle ground that works for you. I moved here from the small town where I grew up, and while I would not want to live in the district and I don't always think happy thoughts on 495, I think it is a decent place to live. And for the short term, and adventure.