Pull out of oven, cookies fall apart again. We can't roll them around in the sugar. Pull off of pan and let cool a bit. Cookies can be fragile when hot. 5 minutes later, cookies still exploding when picked up. We managed to get 8 cookies out of that 2 dozen batch.
Make third pan. Remove from pan immediately, though carefully. Dredge in powdered sugar with a dredger (small container with a close mesh). Let cool 2 minutes then roll in sugar second time. Only lost 2 cookies in that batch.
But still, they are waaaaay to fragile. If you don't pick them up very carefully, they explode. After doing a bit of research, I think I'm going to add an egg and (possibly) an egg white. The whole egg will add moisture ('cause they are a bit dry) and strength (to keep them from exploding). The white adds strength, so I might throw in an extra one of those. I might try making another half batch with egg to see how well that will work. (A full batch makes almost 9 dozen cookies. But I can get 2 dozen per pan, so it goes fairly fast.)