I don't know for sure, but the step-children thing is possibly a cultural/religious difference.

In your culture, it may seem the most natural thing that the child stays with the mother and so when the step-father gets a job in the Middle East you would assume that since your own culture/legal systems favour the mother having custody of the children and being the main parent, you expect everywhere to operate by the same cultural and legal traditions you do. Under Islam that isn't the case, in Islam, the father is the guardian/custodia, i.e. main parent, they are his responsibility.

If children are expected to live with and accompany their divorced mother and step-father, that isn't the way things are done under Islam. Under some Shariah (I don't know if it's a general thing) a boy child could live with his mother until he reaches the age of seven, at which point the custody passes to the father. For female children, they would remain with their mother until puberty, and then custody would pass to the father.

Taking the step-children away from their father in their home country would not be the norm under Islamic law, so it's probably not something that's accounted for under Qatari shariah (Islamic law) -- although I don't know the Qatari shariah, I'm just extrapolating.