There's another extremely good reason to monitor her texts...she's very vulnerable right now to a predator. She's confused, her father is trying to co-opt her by alienating her from you, and she's already not being honest with you ("I didn't realize he was drunk.")
Counseling for her ASAP, if she isn't already going. She's going to hate losing her phone privacy and he's going to make you the enemy even more. You'll need to stay strong and you'll need help with your daughter.
Sending you a hug.