Bull. Do not be passive aggressive and stand up for yourself and TELL her she must ask you if you are agreeable with this. You hired on to take care if her child not her friends children. I would have told Ella's mother that it was not possible or, alternatively, your hourly fee for babysitting her kid as this was not a playdate.

Tell her that you had a plan with your charge that you had to change to do this. If she could let you know in future so you know not to make plans you would appreciate it.

She normally checks that its okay for me to pick up one of my charges friends if needed. Yesterday a mom at the school said to me "Can I just thank you for agreeing to look after Ella tomorrow afternoon?" I didn't know what she meant and said so. She then replied with "Oh. Did Jane (MB) not ask you if it was okay?) Turned out Jane had said I would take my charge and Ella home tomorrow instead of checking with me first. I felt embarrassed and annoyed.
How do I approach this with MB?