The law does not mandate who is responsible for transporting a child to or from the visiting parent. Consequently, unless the court order which grants visitation outlines the rules about who is responsible for doing this, it is up to the parents to work this out between themselves. The language chosen, "regardless of inconvenience" is far to vague to have any teeth.
If your court order for visitation does not specify exactly what you are entitled to and in what manner or place you are to get visitation, then you should consider modifying your current visitation order.
Keep in mind that no one can take the place of the advice, counsel and experience of an attorney licensed to practice in your area.
Generally, you must wait a reasonable amount of time. So what is that amount of time? It is not listed in the Texas Family Code. So it is up to the Judge in your case.
You might want to sit down with an attorney that is familiar with the Judge and discuss your options.
Generally, I say to error on the side of being reasonable and accommodating. If the persons calls and says that they are running late, that is nice so I encourage you to also be nice. I encourage parents to work together whenever possible.
If he or she does not call, then an hour is reasonable. After that time period, you are free to go on with your life. You are not held 'hostage' all weekend.
If you read your decree, most state that all visits are by mutual agreement and the Standard Possession Order is only followed if the two of you cannot agree -- otherwise the two of you can do whatever you want to do. I always encourage parents to work together because it's easier on everyone -- including the kids!
Since I've never met you, don't rely on this advice! Talk to an attorney in person! Sit down with an attorney who should read your current legal document, can give you advice after finding out who the judge is in your case, and who has reviewed your file.
You might want to try mediation and see if the two of you can resolve your issues without going back to court. I always encourage parents to work together & not spend a lot of money because that seems to make everyone upset!
You are not required to sit at the house all weekend waiting for the person to show up. However, if the parent shows up and you are there, you must release the child regardless of how late they are. It is not up to you to decide the reasonableness of the explanation.
Remember what a judge will be thinking - this is about the child and the child's right to be with the other parent. Just because the other parent is somewhat irresponsible, or at least disrespectful to your plans, does not mean that parent is unimportant in the life of the child, or that a judge will be pleased if you cause problems that interfere with that relationship.
There is no defining time limit. If this happened once or twice, then it should not be a big problem. If it happens every time, then that is different. If you have plans that are contingent on the other parent showing up on time, tell them. "I have plans this evening. You are supposed to be here at 6:00 to pick up the child. Because of my plans, I need to leave no later than 7:00 p.m. Please let me know immediately if you will not be able to pick up the child by 6 so I can make other arrangements for the child for the evening." Or something like that.
I do not practice family law so don't rely on this advice as law. It is logic. : )