oh sweetie, don't start with the "as a parent i will never..." because that sets yourself up for failure.
If you have a girl you will be doing her a massive favour in sending her to a single sex school. If you have a boy you will be doing him a favour by sending him to a mixed sex school. It is quite the conundrum. Of the people i went to school with, many sent their daughters to our old school. With excellent results.
Good luck with the IVF though, it can be a rough journey.