I never drived on this route before but for sure insha alla will do in july with famiy due to increase in air fair and advanture.
After reading few threads i concluded that Rahim yar khan (Sadiqabad) is the best stop for night stay its aprox 665Km from KHI i,e half way to lahor.
I drive a lot with family and kids from Islamabad to onward (north) and based on this experence specially with kids i don't think driving more then 5 to 6 hours a day is good, it become headack rather than tour.
I guess Kn_KHIPK or Libra can advice more specifically as they have experence with kids (kindly comment)
Found from map
Karachi - Hyderabad 175 Km
Hyderabad - Sukkur 315 Km 490 Km
Sukkur - Rahim yar kan 17 5km 665 Km
NIGHT STAY
Tahim yar khan - Bahawlpur 185Km 851 Km
Bahalpur - Multan 93 km 945 km
Multan - Sahiwal 175 km 1110 Km
Sahiwal - Okara 40 km 1150 Km
Okara - Lahor 150 km 1292 km
Some Distance are apporximate and some from Map