Well, you already got good advice from other forumers. I'll just add my few cents from experience.
1. Weather: Cold even at the best of times (night time that is). March is a no go time as even locals descend to lower grounds during winter. June is the earliest you should consider but if you want to see it in full glory then late july or mid august is the best time to visit. On the down side, its the monsoon season so travelling in northern areas during wet conditions can be dangerous. Plus, a cloudy day doesnt make for good scenery.
My advice: Travel either last week of june just before monsoon or in August but find a window of good weather but check for forecast from met dept.
2. Road: KKH is fun and the most developed of the two alternatives (though not in a great nick). The other one is via babusar pass and on to Chilas. Any car can go by KKH but you need a jeep (or rented high clearance vehicle) for babusar pass. Babusar is shorter but due to jeepable track, its also slow. On the plus side, you get to see Naran, Lulusar and Babusar top en route. A slight deviation and you can visit Shogran and Siri Paye too (worth seeing).
Remember that whether you are going via KKH or Babusar, on your own car/jeep or commercial traffic. They will only take you as far as Raikot bridge. From there, you MUST hire local jeeps that take you upto tatoo (a villiage) followed by a hike to fairy meadows (and beyond).
3. If you are coming via Naran side, there is enough to see en route as I mentioned earlier (Naran, Lulusar lake, Babusar pass, Shogran and Siri paye with a little, half day, deviation). Otherwise, Rama or going on to Gilgit could be alternatives depending on time and budget. If you are a hiking sort of guy, a full day excursion to Nanga Parbat base camp (which is what we did) can be added.
4. Reaching Fairy Meadows from Tatoo villiage (last point of jeep) is a strenuous and demanding trek. Can possibly take an average (good shape) hiker around 4 hrs and for the out of shape up to 6 hrs. It gains significant altitude and is rather tiring unless you're used to it. I am not trying to scare you but just letting you know that is more than " a little hiking with kids".
All the best.