You said that if you turn all of your plugins off the problems fixed, so that’s the first place to start.
Disable all of the plugins to start with, and then re-enable them one-by-one – and check to see if you can move the widgets between each plugin that you switch back on again. If you do each one in turn and test between each one you’ll find out which one is causing the problem. Once you know that you’ll be able to ask more specific questions about what’s happening.