Remove son's Bluetooth device from my phone but not the account or his phone

Give him his own apple ID and use Family Sharing for app sharing. He doesnt need a credit card to have an apple account.

I still do not share bluetooth devices In the account like you but maybe Apple Beats are classed as an Apple Device.

Tap the (i) and say forget for "normal" BT devices

As it has been already pointed to you, your issue is due to fact your family is sharing one Apple ID to access iCloud. If you don't want to have this problem, start using the Apple ID service correctly.

He's a minor without a credit card! How else can I authorize and manage his devices (rhetorical)...THANKS, BUT NOT HELPFUL AT ALL!!

Set up Family Sharing: https://support.apple.com/en-us/HT201088

Request and make purchases with Ask to Buy: https://support.apple.com/en-us/HT201089

Use Screen Time on your iPhone, iPad, or iPod touch: https://support.apple.com/en-us/HT208982

First part of the question, Are the Beats nearby? They will always be offered for connection if in range.

e.g. The "BT docking" device below is not set up for connection but simply in range. It appears on my iPad.

The "M430" and the "Vauxhall" do NOT appear on my iPad.

You can use Family Sharing.

See this article: https://www.apple.com/family-sharing/

Stop sharing an iCloud account. They are NOT meant to be shared.

That's the root of your problem.

Great.

I'm afraid I never owned Beats and they obviously behave differently to third party devices.