Since my last post there were several occasions where syncing to my ipad2 did not work again. I finally contacted apple support via chat. The steps that helped me get those playlists synced to the affected device are:
1) With the affected device connected to itunes on my mac, in the screen showing which playlists are synced to that device de-select the playlists you are trying to sync. (Originally I was syncing entire library to the ipad2. I first had to change that to "selected playlists only", then select everything except the affected playlists.) Then sync.
2) Step 1 should remove the affected playlists from your affected device. If so, proceed to step 3. If not, with the device still connected to itunes on mac, reboot the device which for the ipad (or iphone) is to hold the power button & home button down at the same time until the screen turns black. Once that happens you can release those buttons. The device should restart by itself. (If you don't have it connected to itunes, it may not restart by itself & these steps may not work.) As the device boots back up, itunes will try to connect to it but may not be successful as the device is not fully ready and therefore showing you a pop up message on itunes to that effect. Should this happen, just wait for the device to be fully up, then enter the keyboard password if there is one on the device, then click "try again" on that pop up message from itunes. Note that after this reboot, the affected playlists that you are trying to remove may still remain on the device even though according to itunes on mac in the "on the device" section they are no longer there.
3) On itunes on mac, re-select those affected playlists and re-sync.
4) If step 3 does not put back those affected playlists on your device, follow step 2 to reboot the device while it is still connected to itunes and then try re-syncing again.
Because with iOS 9.3.2 on the ipad2 every sync with my ipad2 now takes 5-10 minutes (but with my ipod nano & iphone 6+ sync seems instantaneous in comparison), I have only tried this process twice. Once to get my recently changed playlists onto the ipad2 and once more on a different playlist to see if I can reproduce the result. The first time I did not have to take step 2. The second time the de-selected playlist never got removed from the ipad2 even after rebooting. I have so far, touch wood, been able to sync my nano & 6+ without resorting to any of these steps.
The combo of itunes 12.4 (I'm using 12.4.1.6), el capitan (I'm using 10.11.5 (15F34)) and ios 9.3.2 certainly is buggy.