Thank you for your question. Different expert here as your previous expert opted out. I am sorry for the delay you have experienced.
If the mother will not allow you to see the child and is also violating your son's custody and visitation order with the child, it is your son who is going to have to take the first action. Your son has to file a motion for an order to show cause for contempt of court. As part of your son's filing against her for contempt of court, you will have to file a motion for visitation under the grandparent's rights law.
Unfortunately, the Texas grandparent's rights law has been significantly weakened since the US Supreme Court held in the case of Troxel v. Granville that the parent's right to make decisions for the best interests of their child is a fundamental right. This means that in order for you to get the court to order grandparent's visitation as part of your son's visitation, you would need to prove (as you said above) the extensive relationship with the child since the birth of the child such that relationship should be continued in the best interests of the child.
Generally, in a situation like you describe, especially with multiple baby daddies, the court is going to seek to allow the child visitation in an actual stable home and if you prove the continuous relationship with the child, this will be all the court needs to grant you such visitation.
One word of caution, the child is now approaching the age where bathing with you is becoming inappropriate, so that behavior is going to have to cease. There is no set age in the law for this and child protection
in their investigations looks for intent and harm as well as the cognitive ability of the child and once the child begins to get to the point where they begin to develop their cognitive skills, 4-5 years old, that is when bathing or showering with adults needs to come to an end. This is not saying you cannot bathe the child, but being in the tub or shower with the child (unless you are in there with a bathing suit on of course) is going to at the very least raise the eyebrows of child protection if she were to make such a complaint. However, to try to ease your worry, if this is all she is accusing you of, this type of allegation almost always ends up unfounded and dismissed by child protection (the problem is not that you can face being charged with any abuse, it is that even an unfounded child abuse
complaint can go on your CPS record and there is no removal process from a child protection agency record).
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