wow, that is one confusing setup. LOL
I can understand the overflow part but not sure about the skimmer and the extra line from the aqualifter. Is there a pump attached to the skimmer? They might have set it up with the power from the overflow running the skimmer too.
If thats the case you can get a pump for the skimmer and just have it run normally without extra hoses.
Wish I had a more definite answer for you, but I tried.