Masha Allah, very doable and logical itinerary. I don't know if you have been to Skardu before but the city itself is of no interest. While you intend to stay the nights in Skardu city as its always convenient to be stationed in one place when with family, I would suggest a few adjustments.
You can add Shangrila to either of the days i.e. while going to Skardu or returning from there. Its just on the way. Preferably add it to the day while going to Skardu.
And on return, rather than going to Gilgit all the way back (as you have seen it already) try breaking journey either at Jaglot or even better at Chilas. Chilas will leave you with both options the next morning, either to take KKH or Babusar and you can stop to see more places that had been skipped on the way up.
Secondly, by leaving Chilas in the morning, you can comfortably make it to Islamabad. These two changes will get you two extra days.
Add Shigar and cold desert to one day.
Put Mathoka waterfall, Khaplu & Machlu on one day. Other than the famous forte in Khaplu, try to visit fruit orchards of Machlu across the river via one of the longest suspension bridges. Its a rocky track after bridge but easily doable by car. Just keep it very slow. The same track leads to the last village of Ghanche dist. where wheels can reach, Hushey. Thats a pure jeep track (not difficult but uneven for car). I would have highly recommended that if you would be interested in yet another jeep hire. And a night stay there is a must to feel one of the quietest places (like Deosai).
As for adding Astore...Once you have reached Sheosar from Skardu side, it almost fully covers Deosai. Thought the road between Chilam chowki and Astore is one of the most scenic one, it will be too much to reach Astore (an untidy town) and go back to Skardu. Had you been on your own 4x4, it would have come naturally on the way. The adjacent valleys of Astore and Rama are the places to see but that requires atleast two days.
Temperature in Skardu will be very pleasant cold during the day so no worries at all.