If WOL is working on your internal network (even if its thru wi-fi your still on internal network) then maybe your problem is with your global IP ? Or Windows Firewall perhaps ?
Check with one of the many webpages for your outside ip and see is it the same as your computer you are trying to awake .

One other solution (if you dont have outside static ip) is to set up a small machine and put some kind of remote control app (teamviewer , radmin (radmin will need static outside ip too) and with your phone connect to that small machine and from it WOL any of the computers you need .