They are foreign students so technically they should pay a fee to attend school. You should expect that fee to be around $12K per child per year (this is for public school).
However how this rule is applied seems to vary from school to school. Contacting the school board won't help. You need to get in touch with individual schools in the area she lives in to see if they will allow the children to attend and if so, whether they will charge tuition.
Based on what I've seen on this forum, most schools will charge tuition but sometimes you can find ones that won't.
Also, based on what I've seen on this forum, schools tend to be more flexible with the tuition if one parent is a Canadian citizen or PR. Schools tend to be far less flexible if the parents are here on study or work permits.
I would assume that you will have to pay tuition for both of your children to attend school in Canada.