Terry
I think this is less of an RStudio/R issue and more of an issue of what kind of association there is between the variables you're interested in. I know that's not of immediate help to you, but it would be good to grab the closest statistician you can find, sit them down and talk. Lots. The power analysis part of the problem will come after you've decided on an appropriate analysis method. Having said all that, once you've found a suitable analysis method, there will be a power method available, or an approach, that you can use from R, although you might have to do some custom coding.
Good luck!