I (29F) am the proud aunt of two amazing kids, Chloe (7 y/o) and Harry (8 y/o).

I get along really well with the both of them and their parents (My sister Amber (37F) and her wife Kate (38F)) ask me to babysit them sometimes. We have a special bond

The other day, the kids Amber and I went out to the park. Kate wasn't there because she is a general surgeon and her work-life balance is nonexistent at this point. Kids were playing together in this playground area and Amber and I else were sitting together having a chat.

We heard a scream and rushed to the kids. It turns out Chloe fell and was crying holding her arm. We both freaked out. Together, Amber and I took Chloe to the hospital that Kate works at. They took an x-ray of Chloe's arm and everything.

After Amber trying multiple times and finally reaching Kate, she came down to the ER. She took a look at the X-ray, talked to the ER doctor, and without letting even the slightest bit of emotion or compassion toward her crying daughter and wife, said it was just a small fracture, that it didn't extend to the joint and would be okay in a few weeks' time with just casting.

The only compassionate thing she did was holding Amber when they got Chloe's little arm into a cast. I got really mad at Kate and said she was downplaying her daughter's broken arm and acting as if nothing was wrong! She simply said kids get injuries like this a lot and there was nothing extraordinary going on here.

I may be TA here because I called her an ice cold insensitive mother. Amber got so mad she practically kicked me out of the ER and said she'd go back home with Kate and the kids herself. She said I'd better apologize to Kate before coming over to their house again.

So was I TA for expecting a more human reaction? Should I apologize?