I put a tracker on my mother's phone
Why are you tracking her phone.
I feel it's my duty. I'm also very worried about her safety.
I know you care about your mom but you shouldn't track people without their permission. If you want to track her, get her permission.
I was thinking of all the possibilities that could happen to her.
Ask her how she feels about it then. If she agrees, then it is fine. To do it without her permission is like you don't trust her at all.