Sir, A piece of advice DONT DO IT. It'll be next to impossible to attempt this route on a car with a spouse. The road beyond Jhalkhad is best suited for a 4x4 and high ground clearance vehicle only. For starters there will be steep inclines, rocks, boulders, streams with vintage wooden bridges, muddy tracks and bends and turns that your CITY simply cant handle. Not to mention there will be possibly some glaciers you'll have to cross also. Even if by some miracle of God you do make it to Chilas, the road (KKH) till Giligit is non-existant these days, as its being rebuilt and has been dug all over by the Chinese. Work continues day and night. Also keep in mind that July is monsoon season. Landslides are a major threat. Last thing you would want is to get stuck on Babusar track in your CITY in heavy rain.
City 2010 is a car best suited for city or intra-city driving only. If you want a comfortable ride to Gilgit, then I suggest you buy air tickets because there no such thing as a "comfortable ride" on this particular route, even on jeeps.
Regards.