I went and talked to director of Fethiye Government Hospital today.
They put the new button as "Online MHRS" on the left-top of web-side (
http://www.fethiyedh.gov.tr/)...that will connect you directly to 182 online about the new system.
Everyone can register once and use the same password whenever need to get appointment after that.
Another good news: you can get an appointment(s) in long term which day/hour is available to you...they will also try to put the English version soon...
Fethiye G.Hospital is planning to build the new front office to service for expats only.