I am a home daycare also in Laval and am at $7. You cannot make your daycare subsidized. It is a private daycare. If they choose to, they can apply, but it takes a loooooooooooong time.
I don't doubt that it's better than a CPE. I'm not a fan. I guess it depends on which one, but when I was feeling overwhelmed with my 4 year old son at my daycare I did go visit one since he was offered a spot. He ended up staying with me. Not my cup of tea.
Anyways. Ask the directrice if they have intentions to become subsidized or not. That's about all you can do. Glad you found a place that works for you and your kids, though.