How do you remove the tub/shower diverter?

My elderly parents have mentioned that's it difficult to switch the water between the tub and the shower because the diverter is too stiff. Their home was built in the early 60's and has the diverter between the hot and cold taps. The diverter rotates 180 degrees to switch between the hot and cold.
I went to their house to started to disassemble the diverter. The disassembly started out like a stem faucet but when it got to the point where I'd unscrew the stem (diverter) it wouldn't unscrew. That makes some sense, I think, since the divertor doesn't operate like the taps do. What's the secret to removing the diverter? Once I have finally get it apart, what's the secret to restoring smooth operation?
Thanks.
Richard
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"Confidence Shaken......."
It's just stuck. Turn harder. It does come out just like the hot and cold stems.
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