There's a certain landmass mod that interferes with another landmass mod and I want to move the first landmass mod to a new location. How would I go about doing this?

This isn't something that the CS can do, so you have to use a third-party program.
http://projectmanager.f2s.com/morrowind/TESfaith.html is the one I know of.

It lets you duplicate and/or move entire exterior cells.

Thanks, but when I ran the .exe it simply brought up a command window real quick then disappeared. :/

Ok I followed the directions and got https://a.cocaine.ninja/rjaupr.PNG

Ok I got it to work...kinda. The island has a copy of itself located where I wanted it so now there's 2 versions of the island :/