Hubby works in KSA, can I live in Bahrain while awaiting my KSA visa?

Hi everyone! I hope someone can help me with some useful information

My hubby received a job in KSA and moved there about a month ago. He recently got his iqama AND his multi-entry visa too. Yay

Before this, we use to live in the UAE. But when he left his old job, our family (me and our three kids) had to return to Australia where we are originally from.

It was okay at first because the children were on their summer vacation. But now the next school year is about to start in September, and I'm keen to return to the Middle East so that they can begin the next school year without any disruptions (Australian school systems unfortunately go Feb-Dec, not Sept-July).

My question is: is it possible for myself and the children to live in Bahrain while we are await for my husband to finish his probation period and hopefully afterwards get our family visa to move to KSA? At the moment, hubby is on a single bachelor's status.

Is it possible for my children to attend a school in Bahrain (my eldest are in Grades 1 and 3, youngest child is just an infant) without being residents of the country?

Any information regarding a wife and children living in Bahrain while husband works in KSA on bachelor status will be greatly appreciated! Just to confirm, we all have Australian passports.

Thanks!!