Can I run constant power and a three-way switch with three conductors?
There is a way but it is no longer acceptable by code. The reason is the method used will constantly flip the polarity of the hot and neutral lines to the light making either wire and lamp socket parts hot depending on the switches. Edit: This method is dangerous for this reason. The lamp socket shell, which is always supposed to be neutral, can become hot creating a shock or electrocution hazard.

If you can, run a fourth wire. It can be any color save for green and white. I'd go with blue. Make the red and blue the three way leads and let the black stay live the whole time.

Or, Consider a motion detector and leave the red wire disconnected.

Or, Use the red wire for a light only controlled from the house.