Schools here usually does not respond to email inquiry. At the very least you will need to call them. Even if they respond, most likely they will not guarantee a place for. Some of them even require a face-to-face assesment of the student.

A friend of mine have been here for 2 months and as far as I know, he had not been able to secure school for his primary and secondary aged kids for this year summer term (The kids are still in the home country).

Best course of action will be to ask for your (husband's) company to provide a temporary accommodation of 1 to 3 month which you can use to hunt for schools. After that, you can start looking for your accomodation.
As someone mentioned earlier, nowadays to get a house is much easier than a suitable school.

Another thing that you may consider is to use a brute force approach. Apply to as many school as you can (most if not all will require a non-refundable registration fee) and grab the first one that accept. Once you are here, you can always apply and transfer to another school of your choice for the next term or semester.

Cheers
SK