So think of it as 110v D.C.

I think you need more info on the concept. There is AC & DC. Both can work with 2 wires, or paths, for current. We really aren't concerned with voltage for your problem other than to say 12v is usually an automotive DC mode and 110v is a common "household" AC current.
We are concerned with just the 2 wires, or paths, for current. A positive path and a negative path. Don't think too much on AC, DC, or volts. Just 2 paths. In automotive use one of the paths is the frame or metal housings and at places a wire. The other path will be a wire. For your vehicle the negative path, or ground, is the frame & housings. The positive is a wire.
So it's called 12v DC negative ground but the concern is with the 2 paths to complete a circuit.
IIRC, there is a connection, or plug, on the motor with 2 wires in it. Disconnect the plug and test for continuity between the wires in the plug and then continuity in the connector on the motor. There shouldn't be any.
Run a wire directly off the negative battery terminal to the body of the window motor. Then run a second wire off the positive side of the battery and briefly touch it to one of the two connections inside the plug. The motor should run. Touch the other side of the connection and the motor should run backwards. If the motor doesn't run at all it's probably toast and needs to be replaced. If it runs in one direction but not the other look for obvious breaks in the wiring but you'll probably need to replace it.
If it runs in both directions then check & clean the connections between the quad button and motor.
Report back with what you find
If you think it's the switch then give it a good cleaning and see if it works.