Sorry about the late response. The Raspberry Pi 3 can actually support more than one Audioplayer at once. Wich is why we created the plugin MultiSqueeze to run multiple instances of Squeezelite on one Pi.
The dropouts of the radio might be connected to your internet connection if the playback of local music files does not produce any errors. You might want to try that out in order rule out this source of error. Also, you could try to use a LAN connection if you are currently using WiFi.