Sounds like it might not be a good fit. The early hours is one thing, but the erratic schedule and the child being under 2 makes it not a good match.

In my opinion with the new bill any one under age 2 needs to be full time. Otherwise long run you'll end up with empty spaces. The over 2 spaces will be harder to fill so you can be more flexible with part time or different hours but those under 2 spots should be saved for full time clients.