Are either of you familar with kodi or remote access /streaming via ssh ? If so one simple option would be to setup a ssh tunnel thru to a music store on your network and have him connect to it via key (preferred) or passphrase ( less preferred for security but doable). that way you would be able to update and / or curate playlists and or even allow him to remotely access a pandora /spotify account form your network / IP and not be technically voilating ToS.
Considering there's no one technical on the other end to set stuff up, your best bet might just be to mail him a simple stereo and weekly mixed CDs.
Can you load up a cheap tablet with songs and send that to the caretakers to press play?
not sure if it still is the case, but last time I checked logging into Spotify from a second account begins to control the other logged in account, complete with stopping and starting play.
Remote access like team viewer etc
Sounds like a job for Icecast to me.
Why not get him a tiny cheap media center PC or chromebook or such? You could probably even do this with a Raspberry Pi. Hook it up to a nice set of PC speakers. Set up remote access to it for yourself.
Then you can either download a selection of music to it or set it up to play from a streaming service just as you would on your own PC. If your dad wants to turn it on or off (or the caretakers need to), he can use the volume/power knob on the speakers.
Or if he likes a popular genre of music (classical? Classic rock?), maybe just get him an FM radio?