Generally Tanajib if you are on family status will be on a Sunday-Thursday basis. Either fly from Dammam (40 mins from RT or Dhahran) or drive (2.5 hours or so by car from RT).
They may offer you family status straight off the bat, or they may wish you to complete 6 months trial before it is offered. Most often the preferred route is that you come over and then begin the Visa process for your family (takes a few months usually). If you are offered family status immediately then you will be awarded a house, generally in Ras Tanura.
As to schooling, Aramco schools only go as far as grade 9, so if you are on family status then your oldest will either have to school outside of Aramco (BISAK & British Grammar (both UK curriculun) or Dhahran High (US) all in Dhahran are the main options. There are other international schools, but those 3 are the normal choices for expat kids.
The other option is that your eldest attends school out of kingdom under the Education Assistance Plan. This will help with costs towards schooling, with boarding school being an option. I wont go into too much detail on a public forum, but basically Aramco will pay 90% of boarding or tuition fees up to a cap for private schooling, either boarding or live out if you have family who can help out. Also financial assistance for flights 3 times a year. There are some very good boarding schools available providing a very good opportunity for your child - if you can get family status immediately.
Personally given your circumstances I would be looking at boarding schools now, get your child enrolled and switch to Family status / EAP at the first opportunity. It's a big step for any child and family and not one that suits for everyone's circumstances.
For your other kids, Aramco schools claim to be in the top 5% of the US school system and do provide a good environment for children to excel. My daughter only attended grade 9 at Dhahran before moving on to boarding school in the UK, and I had no complaints at all about her time there.
