If you get legal full custody, it does not stop visitation, and will not end the denigration of your family.
1. That said, if you get custody, what does the child gain from it? That is the most important question.
2. If you get custody, what do you gain from it?
3. Is it worth the legal costs you will suffer?
What is your motive?
Might it be better to control what you can- you- and put the effort into being the best role model possible.
Been there, done all that. Cost me $80,000. Then she started Round 2, which I'm "winning" and she is going to lose a lot of ground- and I've spent $20,000 in two months. What I can say is allegations made by responsible adults over time do win trust, while allegations by a nutjob eventually make the nutjob parent look like a real idiot. That, of course, will be taken into consideration, perhaps unstated consideration, depending on the law guardian and the judge.
BUT without concrete evidence of seriously dangerous behavior (e.g., DUI conviction, abuse, etc.) I don't see where much will change for anyone.
I'm not a lawyer, I just pay one.