External Hard Drive Trouble

I tried to move my iTunes from my local drive to my external drive. What happened was that there was a copy of iTunes in the external hard drive and a new copy of iTunes had appeared in the local drive after I had deleted it. The iTunes folder would reappear in the Public Music folder (a different location) and I can't delete it, because then all of the music is wiped from my computer. I tried uninstalling and reinstalling directly onto the external hard drive. Unfortuntely this process started again. I went onto my iPod and checked to see if the settings were the problem, but the songs get backed up onto iCloud.

Please help! This has been driving me insane! Thank you!