Is it permissible for a daughter to trace the source of her father's text messages with a woman, and to track his mobile phone to find out if the relationship is ongoing? Is this considered espionage, given her intention to solve the problem without her mother's knowledge? And can she be provided with a helpline number to deal with the situation?

It is not permissible for your daughter to pry into her father's private matters or look at his personal belongings without his permission, and his phone messages are among his private matters. However, since she has become aware of this, she must advise him to fear Allah. If he persists in the unlawful relationship after her advice, she may inform whoever she believes is capable of preventing him from this evil.