No, unfortunately a remote session would not be viable.
A OS refresh takes HOURS, and requires a backup to be made FIRST, then your HDD wiped, and the OS installed back on.
You need to take the machine to a technician, who you TRUST, and is Apple certified!
This is NOT somethign a casual user could accomplish. ESPECIALLY because your using a MAC, and Apple guards their OS like the POTUS.
If you were on a Windows PC....I would say you could probably handle the refresh.
El Capitan is the newest version of OSX....and you could TRY doing the upgrade to EL Cap.....and THEN reinstall QX6.....see if it resolves the issue.....but im like 99% sure it wont.
YOur OS has been used for almost 4 years now.....and is most like become cluttered, and needs to be REALIGNED (refreshed)
Its like getting a TUNE0UP on a car
Your car will run better, and be more responsive, and will in turn LAST longer too.