Quality fully automatic turntable with a removable headshell. Does this exist?


Unless I ban my kids from touching the stereo, which I don't want to do, I think I need an automatic TT.  Is there a hifi grade TT out there that is fully automatic AND has a tone arm with an interchangeable headshell?  I want to be able to switch easily between a mono and a stereo cartridge.  
varchard
There are many older fully automatic Duals that can sound very good. And if for the purposes of having others use it many are fully automatic - they will play the record from rest to record end with no need to touch the tonearm.  Many also have removable cartridge mounts for switching cartridges. I have a Dual 1219 that I bought from Fix-My-Dual tha to use alongside my Prime and SL1200 that I like quite a bit. 
A 330 Trio KP 800 might be one that is off interest.

I recently looked at one with a SME Bayonet Attachment Headshell on the Tonearm.
No unless you customize one. That’s like asking for a Model A with a paddle shifter.


That 1500C is as close as your going to get to auto with a detachable headshell. Teach them to use the cue lift or stay away.
Technics 1500C turntable.  Auto lift at the end of record, priced under 1500 bucks. Brand new model gotten good reviews. 
If you are looking for a stacker you will have to find an old Dual in decent shape. No removable head shell though. I do not recall any fully automatic table with a removable head shell. Frankly, I would use my technique. There is only one person who can go within three feet of my turntable, me. Everyone else is limited to digital. 
Audio-Technica (really just mid-fi). The Technics Sl1500C is high-end but autolift only. Buying a used fully-auto Technics is my suggestion.