Alright, I figured it out!
Instead of making an alias, you have to make a "symbolic link" which is kind of like an alias with a few differences in how they work.
For instance, when I made the alias, I just clicked on the Mail folder and made the alias, and then moved the Mail folder to its new location.
Doing the same thing with the symbolic link will destroy the link. So, you have to first move Mail to its new location, and then create the symbolic link where it used to be.
The terminal command is "ln -s [old path] [new path].
You can get the paths easily by dragging the folder/file into the Terminal window.
So, to summarize, I accomplished this thing by moving the Mail folder to NEWFOLDER. And then typing in the terminal:
"ln -s /Users/USERNAME/NEWFOLDER/Mail /Users/USERNAME/Library/Mail"
I hope this helps someone out!