Like Denise said, I'm sure Disney will let you book a "two-fer".
How it would work probably depends on your team host hotel stay. You know when you make a reservation you have to specify the names of all people on the reservation. And the whole Magic Band/FP+ thing complicates the picture.
DH can consider doing this two ways.
1. Make a Fort reservation for the entire length of stay for him and DS and then when you and DD wrap up your team stay, add the two of you to the Fort reservation mid-stay. Might be hard to plan FP+ for your family time, though.
2. Make two Fort reservations of the same type back to back. The first is just DH and DS. The checkout day of the first reservation is the checkin day of the second. On the second reservation you would list all four of you. That might be easier to plan FP+, etc. for your family week. DH may have to go up to the office to checkout and checkin again for the second ressie but as long as they are the same type (both Premium for example) the trailer could stay in the same site.
I've been the band dad at the Fort shadowing DW and the kids on a WDW school strip before. No WAY you could get me to go with the school kids as an official chaperone.

Option 2 requires a second deposit but it's the same expense in the end and it's cleaner in trying to plan your family week.
Sounds like a plan though.

It's a good idea.
Bama Ed