The puppet I made in AI results in a character that jumps around

I always suggest flushing the cache when strange things happen, just in case. Hold down ALT (windows) and click the two arrows in a circle bottom left of scene panel.

Are you able to share the puppet? E.g. use the menu “Export Puppet”, upload to say Google Drive, and post a link here in the forums (or direct message me). Some things are harder to debug than others.

I have been able to correct the x y positions. Thank you for that tip1

The problem is that the puppet has a jiggling disease.

She jumps around and won't stay still. I have tried using the pin and even the handle tool but she just keeps jumping around

The head above the stage, you can use the Transform behavior to change the Y-Position to lower it. If its too big, use Scale property to shrink it. Just click on the puppet, then look in the puppet properties panel for Transform, expand it, and you should see the settings there.