Am I the Asshole for firing my sister/babysitter after she ignored my rules and turned my child against me?

My ex boyfriend left me and our 4 kids - ages 11, 8, 6, and 3 - around Christmas last year which put me in a terrible financial position. My sister and her husband - Caitrin and Ian - worked out a plan to babysit my kids for part of the week for a few weeks so I could work extra hours and get back on my feet. They would keep the kids Monday - Friday and I would have them on the weekends. The kids enjoyed it and they got to play with my sister's kids - ages 9 and 7 - so we kept the arrangement going.

This weekend everything hit the fan. My ONLY rule was that my sister and her husband were not to take my kids to their church because I don't know what goes on there. Well, on Friday my kids asked if they could stay the weekend with my sister and she and her husband were okay with it because they were going to a "Family Field Day". I said it was fine. When I got them back on Saturday I was helping my kids unpack and my 11 year old had a card he supposedly made at the field day event. He was supposed to draw his family and he drew Caitrin and Ian with himself and his siblings followed by Caitrin and Ian's kids. I wasn't on the picture.

I asked him about it and that's when I found out the field day was actually a church event. I called my sister. Her excuses were that it was sponsored by the church but was not at the church or even considered a church event which I don't believe. I also asked her about the picture and she said she saw it but didn't talk to my kid about it. I told her how hurt I was because she and Ian are okay with me being replaced in my son's mind.

I hung up and a while later sent her the following message: "Your services will no longer be needed. I'm enrolling the kids in daycare. Thanks for everything."

She asked if we could talk again and I said maybe later. I told our other sister (who lives abroad and therefore is no help) and she said I am being an AH and said I need to talk to Caitrin but I disagree. AITA?