URL NOT showing the web address I want

I built a Wordpress multisite for a school using my own personal domain to work it out since their address was in use and I had to communicate while out of town. Now I'm trying to switch so the school's domain name is visible instead of my domain in the url. I pointed the domain to my host's name servers, added the school's site as an Addon domain and redirected the school domain to go to my personal domain and so - it just redirects to my personal domain and you can't tell it's the school's web address. I just signed up for web forwarding and use masking (still waiting for that to kick in to see if that does the trick). However, after I purchased it the person says it will also depend on whether my system is set up to "allow URL to display frames"... (I didn't understand this).

Do I need to just clone my multisite and move it under the Addon domain (the schools domain)? I talked to my hosting company and they said they don't help migrate multisites. Do I need to do this myself? If so do you have any directions on how to do this? I could dissable multisite and clone it if need be if that's easier I just need to do it soon. If you have any advice I could use a little guidance here. Thank YOU!