Adobe Flash crashes when docking and undocking HP laptop

That set of symptoms isn't totally surprising.  It's generally reflecting the fact that the graphics or audio hardware isn't in the state that we expect it to be in upon resume.  We don't interact with the hardware directly (it's all done through DirectX, etc).  It's happening underneath us. 

If it's switching GPUs (it's going from a high-power GPU when docked to a different low-power chipset when undocked, as an example), that might produce some interesting results and might be a place to fiddle around with. 

If the machine is going to sleep as part of this -- like she closes the lid, it sleeps, she undocks it, opens the lid, and the machine resumes, you might also experiment with disabling the automatic sleep when the lid closes.  That should help to differentiate whether or not it's just the dock/undock, or the fact that the hardware is changing significantly while the machine is asleep.

You can also try disabling hardware acceleration in Flash and/or the Browser to work around it.  It shouldn't matter for general work stuff, but will impact performance and battery life for gaming and video playback.

Disabling hardware acceleration is covered in the video troubleshooting guide, here:

https://helpx.adobe.com/flash-player/kb/video-playback-issues.html

If you're still stuck, please follow the directions in the guide on providing the dxdiag report and additional information about what you tested and saw.