Living in Dhahran tower

That is correct, there is no place for women to drive living in the DT. But if you have a car and drive to Dhahran, your wife can ride the bus to DHA, pick up the car where you parked it and drive around the Dhahran compound.

There is a small play area outside.

Dhahran British Grammar School is about 10 - 20 mins from the DT depending on the traffic.

I think there is a bus to the school.