Using Team Viewer through Router

I am a ham radio operator with my radio and associated computer located in a detached garage.  The radio room has WIFI access through my router as does my laptop in the house.  I am running digital modes, no voice required.  My goal is to be able to go to the radio room, power on the radio and the computer.  Note that the coputer in the radio room can control the radio using a program.  I would then like to be able to see the radio room computer's desktop and run the radio programs from the house computer through my WIFI router rather than the internet. 

Note that for logging purposes, the radio room computer will be connected to and access the internet as will the house computer.

My concern is the amount of data bandwith requred to run TeamViewer through the internet.

I know the above is rather wordy but going through this forum and the Team viewer website it is not obvious to me that this will work.

However, if the dats reuirements are low, my internet connection has a data cap, then it may not be a problem.

Any advice and info greatly appreciated.

Wally