We went through a similar process when our kids were early in grade school, and came to almost the same conclusion. Our circumstances are a little different (two kids, not four) but we had many of the same constraints. We consider a 2BR unit the minimum for the four of us. We were not sure if or when the kids would "age out" of Disney, but we understood that
DVC only made sense if we'd be going back at least once a year for most years, until about 7-10 trips were under our belts.
When we added it all up it seemed like too big of a risk.
However, we also discovered that our offsite vacations were still enormously fun, especially at some of the nicer nearby locations: Wyndham Bonnet Creek, Hilton Sea World, Sheraton Vistana, and others. So instead of buying DVC we put together a portfolio of other timeshares that were
very inexpensive on the secondary market---think somewhere between pennies and a dime on the dollar.
Using that portfolio, we've had some fantastic vacations, all during school vacations (so prime time). A 3BR penthouse in Hilton's Lagoon Tower in Waikiki. A 2BR condo in Old Town Alexandria for the Cherry Blossom festival and the Grand Tour of Smithsonian museums. A 2BR condo in downtown Sedona with some great hiking. A 3BR within walking distance of the beach on Hilton Head in midsummer. A 4BR condo with a private hot tub that we invited friends to share with us in Williamsburg, VA. Oceanfront 2BR condos on Kauai, and a couple more Hilton 2BRs in Waikoloa on the Big Island. Spring Break in a 2BR at Vistana Beach Club on the Southern FL coast. And many more.
We've supplemented our timeshare stays with some cash
Disney vacations:
DCL cruises, a stay at
Disneyland Paris after a week in Paris proper, and we had planned a week in Tokyo followed by a trip to TDR that the pandemic cancelled. We've also used timeshare exchange to access DVC properties. That's become a lot harder over the years, and it probably wouldn't work for you (2BRs are basically impossible now), but cash certainly will!
My kids are now just about out of the house: One starts her graduate program this fall, the other is halfway through his undergraduate degree. Looking back on it, I don't think I'd change a thing. That's true even though the kids enjoyed Disney a lot longer than I thought they would. In fact, it's still the eldest's Laughing Place, and she and I spent her last undergraduate Spring Break in a 1BR at Saratoga Springs early this past March, just under the pandemic wire.