The laws in each state are a little different, but generally children are better off having a consistent and healthy relationship with BOTH parents. Moreover, the studies tell us that fathers who have frequent and continuing contact with the children are more likely to honor their financial obligations for child support, health insurance, medical expenses, education and even alimony. There are even a few states (not most) that allow a parent to stop paying child support if visitation is withheld. You need to check the laws of your state with an attorney in your state. Parents need to be really careful not to influence their children's thoughts about the other parent. Kids pick up on not only what you say about their other parent, but also the way you say it, your tone of voice and your body language. Most often, if the primary parent encourages and supports the kid's relationship with the other parent, the child will want to go, and that will be good for everyone. If it continues to be a problem, i suggest you and your daughter get into counseling--and invite Dad to come as well. A good mental health professional will have seen something similar to this before and should be able to help.
I am a Washington and Oregon licensed attorney. In these states, a child does not get to decide this. In some circumstances in the states I practice in, a custodial/primary parent can be held in contempt for not requiring the child to go on the visit.
The prior attorney posting on your question has given you good advice. Some other thoughts:
Your question doesn't provide me with enough information about why your daughter does not want to visit. The reason could be as simply as she is having an adjustment problem that can be readily solved with two parents working together to solve it. Or it could be more complicated than that, and involve her feelings of safety and security. Maybe you don't even know what the true reason is, because children of that age (as you well know, being a mother an all) may not be able to articulate what's happening in a way that an adult can readily understand.
So first, you should consult with your child's father about this situation to try to problem-solve it together. If you don't think you can do this, I'd recommend you engage with a mediator in your area to help you and your child's father talk about these difficult issues. The mediator should be one who specializes in conflict resolution and understanding family law/parenting/child development issues. This person will probably NOT be a lawyer, though that is not always the case of course. If you don't think your child's father would agree to mediate, then you investigate mediators yourself and call them to ask them their ideas about how to engage your child's father in this process. Don't let your child's father's reluctance to engage in this process stop you from researching it and learning about ways to help him feel comfortable and safe about mediating issues with you.
Another idea may be to begin counseling for your child. Your court order may require joint decision-making on this issue, and/or may require notice to your child's father of this. So check your orders and the current state of the law in Texas before moving forward with this idea. This idea can also be mediated if you are concerned about whether your child's father will agree to this or not.
The issue is not going to go away on its own - without the help of professionals - and the sooner you and your child's father begin a dialogue about this the better.
While I do not practice in your state, I can tell you that as a practical fact, judges tend to be quite critical of custodial parents who allow or encourage their children not to visit their non-custodial parent.
If it is in your child's best interest to maintain a relationship with both of her parents -- and it requires her to go in the court order based upon an agreement or a judge's decision -- then just as you would require her to look both ways crossing the street and go to school daily and not eat anything harmful and do her homework, etc., then YES, you must make her go because both of you must follow rules even if you do not always like them. Do not help in alienating your daughter from her father.
The short answer in Washington State is that "YES" your daughter MUST GO VISIT WITH FATHER. Unless there is something going on, making father's home or environment something that will negatively impact your child. That could be that the father is a druggie/alcoholic/mental patient.
Court's decide what's in the child's best interest. To modify an existing parenting plan (in Washignton) your ex-huband must prove that your home, or your parenting style, are a negative for the chil (that you're a druggie/alcoholic/mental patient). That means, ex-husband must prove to the court that you are an "unfit mother".
The simple answer is yes, you must make her go. As in other states, Indiana law takes the position that you are the adult, she is the child, and she does not get to decide whether she wants to go to her father's or not--just like she doesn't get to decide whether she goes to school, whether she does her homework, or whether she does anything else you've told her to do.
You should NOT, however, tell her that she has to go because "the judge said so" or anything like that. I've seen some parents explain that if the child doesn't go to the other parent's home, they could get in trouble or even go to jail. Kids should not be exposed to that kind of information. They do not need to believe they have to do something or else a terrible thing will happen to their mom or dad.
If your daughter insists upon an answer, tell her that life is full of things where we have to do things we don't want to do. There are days you may not want to go to work, but you still have to.
You may also wish to tell her father about the resistance--and immediately also tell him you're not trying to keep her from going, but so that he's aware that you may need to ground your daughter (e.g. no video games for a week) for not obeying you and so that he can maintain the unified front on discipline. Some exes aren't very amenable to these sorts of things, though, so you should use your judgment.