Teaching dog to only engage in playing with people once invited

My dog likes to engage in playing when my partner and I "rough house" such as tickling, play slapping, and kicking around. She'll come over and start barking and bouncing around and we'll join her in and she'll grab a toy and bring it over and play nip every once in a while. This doesn't bother me as well as any adult in my family as she is very gentle with her play biting. The problem comes in with little kids.

My nephew came over for a gathering and was rough housing with my dad and my dog would go over and play nip by pulling on my nephews sleeve and the occasional bark and bouncing around, nothing aggressive or dangerous. His dad tho was very skeptical and nervous that my dog might accidentally nip his skin instead of his sleeve and accidentally hurt him, reasonably so.

This didn't happen thankfully, but it did get me wondering. In a situation where I have kids in the future and play fight with them, I wouldn't want my dog getting involved and accidentally hurting them. My dog is very well trained with recall and still improving. Also fully trained in down stay and place. I want her to be able to continue her playing habits with me and my family as she doesn't pose a threat to any of us, or even a threat to older kids. Its just toddlers that I don't want her to nip and accidentally scare them or pinch too hard.

What would be the most appropriate method to get her to undertstand to not enage with people play of any kind, unless invited. I feel this would be the best end goal as her playing isnt the problem, its controlling who she plays with. I want her to be able to play with me and kids, but only if the kids invite her to join, in which they would be aware of her play biting. (Wanted to emphasize, she doesn't only target kids and is not reactive. She treats everyone the same when it comes to playing)

TLDR: What is the most efficient method to train a dog to only engage in playing with people i.e play bite, bark, and growl once invited. In any other circumstance in which an invitation is not given, they ignore the play until invited.