elliott21:
That being said, would I be able to do this using only one computer, while of course connecting them to different USB ports?
Yes. I do that regularly.
If you just want to use the IDE for uploading programs you just need to select the appropriate serial port before pressing upload.
If you want to use the Arduino IDE to see output from both of them at the same time I believe you need to start two completely separate instances of the IDE - I don't do that myself. When I want to see the output I use a terminal program Minicom - which I think is Linux only. I believe RealTerm and PuTTY work on a variety of operating systems.
...R