The visa officer is concerned visiting as a family means you may overstay your visit. And, the reason/purpose of visit is not strong enough to compel your entire family to visit.Refusal reason is purpose of visit just,
Age of children are, 13, 11, and 9,
Yes they have visited with me Saudi Arabia and Du
Unfortunately, someone/some applicants will need to stay back in the home country. I'm skeptical that all your children will be granted TRVs. Unfortunately again, a number of Pakistan applicants have claimed asylum on TRVs which makes it difficult for genuine visitors to be granted TRVs.
To have any chances of getting TRVs (and I think it won't happen anytime soon), your entire family would need to build stronger travel history to countries like the US, UK, EU, Australia, NZ, etc i.e. short visits of no more than 2-3 weeks on each visit.
You can also order GCMS notes to get the complete notes for their refusals