What was the basis for the court granting you primary custody/residency?
What was the basis (rationale) for his requested custody/residency change?
Does the dad think something inappropriate is happening with his daughter?
Does he live out of state?
Did either of you move? (If so, who moved away?)
Does the dad have joint custody? What is the split?
Does the dad think you are a bad mother? (On what basis?)
Is he paying child support?
What does his wife think of all this?
Are the siblings her half siblings?
How is the father "trying to poison her mind" against you?
How does your support network compare to his?
The fact that the phone call involved a speaker phone with him in the room suggests that he is both manipulative and lacks confidence in his position. Or it may be just a really weird coincidence.
It may be important to understand what is influencing your daughter's thinking. (Is her dad trying to buy her affections? Is her dad bad-mouthing you? Is he located closer to her friends/school/etc.?)
A good lawyer
Offer a safe place for your daughter
-> try and protect her from any tension that occurs between you and her dad
-> DO NOT bad mouth her dad in front of her
-> DO NOT force her to choose between the two of you
-> family counseling will help her voice her thinking
Can you find out what is motivating your daughter here, without forcing the issue?
You don't want a situation wherein you win this battle but lose her heart. If she feels she is being unjustly dealt with, she'll split at 13 (TX rules?) and not look back.
In the meantime, prayers for everyone involved.