If you do decide to approach her about the unkind texts then starting off by telling her you understand your actions of snooping isn't appropriate and explain why you felt you need to.
This won't make it any easier, but it may allow you then to bring up the bigger issue. Her feelings for your family.
Good luck this could very well test your relationship. If you have to snoop around and she has to lie then there are apparently deeper issues going on.