Half days are so hard for a day home to accommodate because it's a sure-fire loss of income to most people - simply no one else wants the opposite half of the day. I always hold on for a full day child vs a half day child.

Also, more than 4 hours of care is normally considered a full-day rate, at least in my area. Not sure if that's true across the country.

You might be able to find a day home provider who has their own children in school, if you live in a province where household children count in the ratios. You could then try and negotiate for that space as long as you understand you wouldn't be able to drop off before the household child has left for school in the morning, and must have picked up your child before the provider's child returns home. Also, school closure days when the provider's child is home, you would need to understand that they wouldn't be the open of care on those days. Depending on what hours you need, this might be your best bet.