Part-time jobs that fit around childcare - 23 weeks in

I am looking for part-time work that fits around school hours and found a few evening shifts near Boston. This is my first time dealing with any of this. They can give a schedule two weeks ahead. Is the schedule really fixed?

Thanks for writing this out. I went through something close to it 8 months ago, and it got easier once I kept a simple log of every call and form.