I live in an area where the temperature isn't so much the problem as the humidity and I've been turning on the AC only so that it will pull the humidity down. I found out that whole house dehumidifiers exist but would it be cheaper to run a whole house dehumidifier or just run the AC?
Also, do geothermal systems when cooling remove humidity?
Whole house dehumidifiers are what your A/C does. There are some thermostats that allow you to run the a/c as a dehumidifier (the 3m Filtrete 3m-80 does this and some more), besides using it as a heat pump, by measuring the humidity in the house. As for Geothermal, it works the same as a heat pump. Instead of a outside unit, the piping from the inside unit runs into the ground either vertical, in trenches, or under water if in a climate that you do not get a complete lake or pond freeze.