Why would it be uprooting them, exactly? Wouldn't they be excited to try out a new city for a few months?
I spent my childhood moving from country to country, OP, and my kids went with me to live in Europe for up to 6 months at a time. We left our house vacant: we shut off the water and went conservative on the A/C and heat, just enough so the house didn't roast in the summer and the cold didn't explode the pipes; and I contracted with a lawn-mowing service.
I would give your sons the choice of living with you, living at the original house, or going back and forth and checking on the house.
Sounds like you will all have a great time, actually