Thank you for helping. This Mac Mini is somewhat built into my living room entertainment center and it's more or less a "jukebox" I use Apple Music for this purpose. Anyway, I really can't reposition things very much. However, I did find the below procedure that allowed me to use an external USB Bluetooth dongle.
With this procedure, I'm able to tell my keyboard and track-pad to use the Bluetooth dongle, not the Bluetooth built into the Mac Mini. So far, this appears to be working much better. Once I find an answer, I always like to place it here in case others come across it searching with a similar problem. Thanks again for helping.
Starting with the external bluetooth dongle unplugged:
1 Turn off Bluetooth
2 Wait about three seconds
3 Plug in dongle
4 Again, wait about three seconds
5 Turn on Bluetooth
Additionally, there's a much quicker way to see which bluetooth adapter your mac is currently using. With your external Bluetooth adapter unplugged:
1 If there's no Bluetooth icon in your menu bar, go to system prefs -> Bluetooth and check "Show Bluetooth in menu bar"
2 With the external dongle unplugged, option+click on the Bluetooth icon in your menu bar
3 Note the sequence of letters and numbers after "Address:". This is the name of your computer's internal Bluetooth adapter. (I usually just pay attention to the last two characters)
4 Now, try to switch to your external adapter, and repeat the above steps. If the address changes, your computer is definitely using the external adapter.