this is one of the wonderful place to visit with family and i hope you will find this trip memorible.. please also see my comments per your questions below;
- My car is Toyota Corolla 2.0D Saloon [Diesel] 2003
your ride is perfect, just make sure all machanical works are checked before you leave.. which is a normal routine..
- I need information about Karachi to Lahore road condition / duration / any stay before Lahore
If you will be going through Lahore, there is no other route option but National Highway-N5, which is good in condition overall except few patches in Sindh.. since you will be with family, it would suggest to stay halfway, may be in Rahim Yar Khan or Bhawalpur.. i dont have any detail about hotels on N5, but some experts can help to provide some guidance..
- Any idea road distance (Km) from Karachi to Lahore then Kaghan / Naran
visit maps.google.com, you can find out distances by location.. very helpful site..
- What is the best route from Islamabad to Kaghan / Naran
Karachi to Lahore via N5, then Lahore onward, follow motor way-M2 till Islamable and then continue to M1 and get exit to Burhan exchange for Hassanabdal and then to Haripur, Abbotabad, Mansehra, Balakot, Kaghan Valley.. above website can provide you complete route..
- What is the Road conditions from Islamabad to Kaghan / Naran
its great overall.. but there are some patches after balakot but those are also managable..
- Advice the good Economical hotel for Family with Hot water and other facilities in Kaghan and Naran
there are plenty of hotels.. you can choose by your own.. last time i stayed in Erum hotel which is in main Naran bazar and also provide good car parking..
- is any problem for small Kids
not at all just keep warm cloths and some basic medicines with you.. weather can change at any time and nights are quite chilly there.. i hope your family will enjoy this weather..
- Any other useful information would be highly appreciated.
since you are going by road and with family.. avoid driving in nights and have good rest.. check all tools, keep one torch and tow rope, recheck all your vehicle's paper and also keep Highway Code of Conduct book with papers as well as also arrange NoC from ACLC.. these two things are really not necessary but sindh police asks them near to sindh punjab border..
wish you a great trip..