Cleaner music when laptop is on battery vs plugged in

I would hazard a guess that when you use it from battery you are not getting all the and RFI from the mains supply.

Laptops are notorious as the worst possible devices to use in Computer Audio, for the very reason cited. May I suggest, as a very inexpensive alternative, using a Raspberry Pi computer with a digi+ S/PDIF card, and eliminate the laptop.

Make sure your USB cable from the PC to the DAC has a ferrite core at the PC end, and even better, both ends.

I personally use a mini Linux PC plugged into the wall, with my audio plugged into a Furman. This keeps the PC supply outside the Furman's noise filtering.
Also, in addition to the switch mode noise, there's been evidence of ground loops occuring ONLY when the AC supply is plugged in and a metal cable is used. Modern USB capable dacs should be galvanically isolated, but this may not always be the case. It is worth experimenting with USB isolators or optical connectors.