If you are comming from Lahore u need atleast 2 days for travelling only. around 7 hours for Abbottabad and i think 3 more for Kaghan so do ur math You won't need A/c beyond Abbottabad and CNG might not be available beyond Mansehra so get ur tank filled with petrol from Mansehra.
I have not been there for a long time now but i am sure you can take ur car to Shogran easily.
Have u ever taken a step forward from Murree, I mean Nathiagali and Ayubia? If not then try these this time without stopping in Murree.Start your journey early from Lahore, go straight to Ayubia then Nathiagali then Abbottabad. Stay there at night.
Next day go to Thandiyani come back and again stay at Abbottabad. On 3rd day spend some time exploring Abbottabad's local places like Shimla Pahari etc and finally back home on time.