May I suggest that you take up this issue with HR (and I don't mean the Clerks)
The pre K child I don't think will qualify for school fees but I don't know. If he/she does then I am sure something could be worked out.
We had kids going to two different schools (Junior and Senior) and it's not an insurmountable problem.
Can I also suggest that you don't get heated with HR. It may result in an equivalent response from HR.
I am sure that HB would receive a reasonable response if he wasn't (apparently) so bombastic.
The art of survival in the Gulf is to keep your cool and be logical