I sympathize with your conundrum! We had the same issue/question at Wilderness Lodge Villas last year. (Although we were a party of 6 staying in a 2-bedroom villa with 3 different beds plus a foldout, we wanted to confine sleeping solely to the bedrooms and the ages, genders and relationships of our party members required four different sleeping spaces in the bedrooms.)
The short answer is no, you cannot get a cot or fold-out bed at any of the Villas. If you Google it, you may find a Disney "Mom's Panel" Q&A wherein the "Mom" says you
can borrow hide-a-beds at the Villas. That is just flat-out incorrect, as I confirmed with several CMs in several departments before our trip, and again at the front desk when we checked in.
We ended up bringing our own twin-sized inflatable air mattress and placing it on the floor of the "master" bedroom. (Deflated, folded up and with a battery-operated pump, it took up about 1/3 of the space in a carryon-sized rolling duffle bag). If you didn't want to travel with one, you could order an inexpensive one from Amazon or Walmart.com, timed to be delivered to your resort a day or so before you arrive. (Just have the name associated with your WDW reservation, and expected arrival date, on the shipping label.)
Another option would be to change up the sleeping arrangement -- put your husband and son on the fold-out, while you and your daughters take the king-sized bed (in a 1-bedroom) or the queen bed + the Murphy bed (in a studio).