You can do this, but I’ll warn you that my mother did this and it destroyed all trust in our relationship. Seriously, not for a week, or a month, it has been 20 years and the trust is still ruined. I didn’t even drink or smoke or anything, I’m still angry at her for snooping on me, not trusting me.
She has never apologized or felt any remorse for tracking me. All she had to do was ask where I was and I would have told her. You do this, understand how your child will react.