Previously: There was no such thing as a car phone in 1910, period.
New timeline: There was, in 1910
The earliest telephone networks were wires laid along the road. Lars Ericsson noticed that you could make a call from a car!
You had to stop, extend a wire from the car, attach it to the cable, and call. Your ability to call, was mobile.
This video from 1949 illustrates the process.