With all due regard to the above attorney, under Texas law your child is a child until she turns 18, (see Texas Civil Practice & Remedies Code - Section 129.001. Age Of Majority) and then she is considered an adult and can make her own decisions.
Until that time, or such time as a Judge modifies the court order, you are legally obligated to provide her for visitation with her father, unless the father agrees to only have dinner, etc.
Until 2007, it was the law that the age of 12, a child could voice their opinion on which parent they wanted to live with, however that law has been abolished. Now, you may file a modification to the custody order, and you can file a motion asking for the Judge to hear your child's testimony on why she does or doesn't want to spend time with her children.
However, until she turns 18, you are legally responsible for her and bound by the court order to obey it, just like he is legally responsible to pay for her child support until she turns 18 or graduates from highschool, whichever occurs later.
Just as a point of information, there is a split in the appellate courts in Texas about if a parent can be held in contempt when a child, typically older, refuses to go visit the other parent. The custodial parent cannot have any hand in the refusal - at all. Some courts will hold the parent in contempt (fine/jail) while others will not. Just because there is a split in the appellate courts does not mean you should allow her to refuse. The better option is to either modify the court order or wait until she is 18.
Disclaimer: This answer is intended for informational and educational purposes only and should not be considered legal advice nor forming the attorney client relationship.