AFTER READING YOUR AMENDMENT AND "SO WHAT HAPPENED".
"He decided to tell her the truth".....What is the truth?
If your daughter "thinks" she will be better off living with Dad, if his home is stable, save the money you will be wasting on attorney fees and let her GO, with the stipulation that she can't be running back and forth if things don't go her way once she's in her father's home.
I would suggest a "temporary" custody order for one year with similar visitation with you. Save him the trouble of filing a motion for permanent custody.
I am concerned that you seem betrayed by a 14 year old, "going behind your back", she is probably unhappy at this time, but I wouldn’t exacerbate the situation by making her a party to “the enemy”. If you are going to counseling I would suggest that her father be a part of the counseling.
Moving to Dad’s
Drinking and molestation addressed in court
What was the outcome when these two issues were addressed in court?
Are you children confused or do they want to go live with their father?
Painful as it may be, it is possible that your children could have some say in where they want to live unless there are concrete/provable reasons why they should not be allowed to live with their father and have visitation with you.
If you can substantiate valid reasons for your children to remain in your custody, I would put my foot down and simply let your children and your former husband know that they will remain with you during the school year and his visitation will remain the same “unless” he keeps pushing for more, and trying to entice your children by offering this and that. Which means you will go to court and have the current visitation modified for less visitation, and the court will order him to stop trying to win the children over with bribery.
Keep in mind, if your former husband can prove he and his current spouse can provide the better (more stable) home and your accusations about alcohol and molestation are unfounded, you could lose.
Lastly, both parents (all parents involved) must address the most important issue; that is what is in the best interest of your children.