Licenses allow for more kids and allow providers to offer subsidy. There are plenty of legal private daycares. Hopefully someone from AB can explain how it works there.
I'm not 100% sure but I would think your verbal agreement would stand. Without a contract I think you might be outta luck!
If I were you, I'd still send him and hit the pavement to find a new job. It would be much easier to find a new job without having a child tag along.