I already have a bachelors degree and am considering getting a Grad Dip Ed. Would I absolutely need 2 or 3 years experience teaching in a western country first, or could I get find work with just the Grad Dip Ed?

Is it true that your children can attend the school that you work at for free?

Yes, I think it would be highly desirable, especially for work at the better international schools. As for getting your kids in for free, I heard that applies at some schools but not others. Others might have fee reductions for teaching parents.

Its more about who you know than how skilled you are to get into the good schools.

I got into an international school on the back of a Graduate Diploma and no home country experience. I was however able to display a solid amount of life experience i.e. I wasn't a fresh faced 22 year old grad, so YMMV.