Let me break it down for you.
The total distance (to and from) you'll cover shall be around 3500 km (assuming Naran is your destination). Considering it's a swift and assuming it's in good shape, the major portion of the journey is on paved motorways where you can easily get a good fuel economy if you drive at 90-100.
So let's assume you get an overall average of around 13km/L (motorway driving + driving in mountainous area)..your total fuel consumption shall be around 250-270 L. So petrol bill shall be between 70k to 75k. Add another 7-8k in terms of toll. So around 80k.
Now for hotel stays and food keep 12k to 15k per day aside and so for a week long trip it shall be around 100k.
Now boot space in swift is a limitation but you can get around it by packing light and smart. The weather in Naran or Swat these days isn't too cool and you don't really need heavy winter clothing.
Keep some cash on top of this for emergency purposes and you can have a good week long tour in under 200k.
If you consider flying then a return ticket for FlyJinnah is around 150k for 2 adults and 3 kids (Karachi to Islamabad). Then you will have to hire a car from Islamabad for 5-6 days which would cost around 40k to 50k...the fuel will be over and above this...hotel stays as well...so this option would take your expenses above 300k.
If you take a train then that would reduce the travel cost by a lot but then again trains seldom follow schedules and that will effect your plan a lot. Green line lower AC for 5 berths would cost you around 80k (return trip). Rest of the expenses would be the same..
So make the best decision for you...but ..but ..but...do the tour! InshaAllah you'll have a wonderful time!!