Road to Naran is very good and safe, no special precautions, just make sure brakes are in god condition and engine cooling system is working perfectly.
Road is good all the way to Naran.
Why you want to stay in Abbotabad, you can directly make it to Naran, Abbottabad will be hot and very boring, mostly the hotels are on main road, and heavy truck movement all the time makes it very annoying.
If you think you need a break and want to reach Naran in 2 days then better stay at Nathiagali, You can reach there in maximum 7 hours from Lahore. I do it even quickly as I don't stop in between.
You can stay in Shogran, skip Kaghan, nothing in Kiwai except a good point for having a lunch. I recommend you to stay at Batakundi instead of Naran. Its just 15-20 minutes drive from Naran. You will thank me later after watching the condition in Naran.
Regarding hotel rates, as it will be peak season just after Eid, rates will be on higher side, and I believe rates will be highest this year due to the ongoing Boycott Murree campaign.
Advance hotel booking is not necessary but for peace of mind you can do advance booking, as I think you are going there for the first time with your kids.
