Screen Mirroring

You ought to simply be able to select it. There should be no need to un-pair or otherwise forget the other TV.

If the TV does not appear as an AirPlay streaming device, start by examining its settings.

Use AirPlay to stream what’s on your Mac to an HDTV - Apple Support

An AirPlay-compatible device will simply appear as an option in your Mac's AirPlay menu bar icon. If it does not, then your Mac does not know it exists.

No need to. Multiple devices can be used to AirPlay/Mirror to the TV. At least that is how it works on the LG TV.