That is rather a long time to spend in just those 2 places in winter time.In Antalya Aspendos and Perge will both be visitable,Köprulu Canyon probably not but...do ask locally as it depends on the weather and if there are enough visitors to make trips worthwhile.Trips can sometimes run in winter,it's all down to the weather conditions.You could also go to Kemer and take the teleferik up Mount Olympos whilst there,very nice spot to visit.
http://www.olymposteleferik.com/en/home/
Also from Antalya you could take the bus to Side which is pleasant and scenic in winter without the summetime hordes :) And if the weather is kind to you perhaps even take the bus to Isparta and Eğirdir for a day or an overnight stay.It is 2 hours on the direct bus from Antalya and there are B&B's open in Eğirdir all year round.
In addition to Antalya and Fethiye why don't you add another place?I have in mind for you Burdur and Sagalassos.There are direct buses from Fethiye to Burdur-which has a smallish but well stocked museum-and from there you can take a bus to Ağlasun for Sagalassos.Swampeastmike made an heroic visit there in January(mad fool!)when it was thick snow... so ideally go in December before the snow hits.This mountain top site is extensive,very interesting and the views are stunning.Well worth the effort of going.From Burdur you can then take a bus direct to Antalya.Or maybe go from there to Isparta and Eğirdir before finishing in Antalya.
Whilst in Fethiye maybe just take the bus for a day visit to Kaş as you originally intended.
Finally I am glad to hear all your problems have been resolved,health and family are important.
