Don_S, do you have administrator rights on your music server?
If you do, there’s no reason RDP shouldn’t keep working on it.
Have you set your music server to use a static IP address?
With a static IP, the address never changes, so you can always connect to it at the same location.
If you don’t set a static IP, the address may change, making it harder to find like moving to a new house without telling anyone. People will keep looking for you at the old address, but you won’t be there.
WGH, KVM switch is a load of expensive hardware with cables everywhere to do a job that can be done without cables and cheaper with free or built in software.