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Well, technically, if the sister was an invited guest, she wouldn't be trespassing. If she logged on to a computer, or to an email account with out permission, that information wouldn't be admissible. Anything that was in plain sight might be admitted if it was relevant. It really would depend on what she found.
The father should be prepared to hire an attorney, but should also know that most states will find that he is the most appropriate person to raise the child since he's the father, barring any criminal activity or substance abuse that might render him unfit.