Hi purpleviolet,
I know someone who works at the International School of London in Qatar (ISLQ) which is an IB school (PYP,MYP, IB). It seems to be a very nice school, with many nationalities and no passport preference.
Yes, the Intercontinental in Doha has ladies day on Wednesday.
I went a couple months ago and it was really quite nice! The pool is right next to the beach so you have access to both. I believe it's QAR 50 for a whole day.