AITA for installing a tracker on my daughter's phone?

Alt acc. Will delete after verdict.

My daughter, 14, in middle school, often goes and hangs out with her friends or stays after school. Because of this we have a rule to make sure she always calls or text me or her dad to let us know beforehand.

Last Thursday she had a club meeting. (She gets out of school at 3:30 the club ends at 4:30 I got to the school at 4:45) so I went to go pick her up and called her to let her know I was there but no answer. I called 3 more times and I was waiting for 15 mins. Eventually I got a little worried so I went to see if the front office was open, there was a teacher there and I asked if they seen my daughter. They called her name over the announcements and we waited but nothing.

I called my husband and asked if he had seen her and he said no. That's when I got scared. We called her friends parents and they asked their kids but they said they didn't see her or last saw her at school.

She wasn't Answering calls from anyone or answering texts and I thought I lost my daughter. Before we called the police we drove around the neighborhood and the places she goes to just incase. We eventually found her walking to a gas station, not far from school.

We were relieved but immediately started asking her questions, why didn't she answer her phone, where was she, etc. She told us her phone died so she just went over a friends house. We knew this was a lie since none of her friends or their parents saw her. Also, if this were true she could've asked to use a phone to call us and let us know.

We kept asking her to tell the truth but it was lie after lie. We gave up and grounded her for 2 weeks.

However the whole situation has made me paranoid so I'll admit, I did take her phone and install a family tracker app. The next day she saw it and was livid and demanded we remove it. I told her no, she not only broke our rule, but lied to our faces over and over again.

She's not speaking and tells me We overstepped her boundaries but I admit that has made me think, dealing with a overstepping mother myself.

So AITA and did I overstep? If I did I'll remove the app ASAP.