I don't know your relationship with your daughter. I assume she sees you as much the boss as mom is?
I would simply say to her:
"I've decided not to permit you to get baptised before you're 18th birthday. The reasons are numerous, and even if it is really your desire to do it before 18, I can't see any possible harm to you from waiting. You wouldn't get to run the microphones anyway *grin*.
Jesus was 30 when he was baptised. I personally was baptised into the JW organization years ago, and I was a firm believer at the time; look at me now, I've changed my beliefs about the organization totally. The same can happen to you, and I want you to be prepared for the consequences.
I don't believe that when you have thoroughly examined your religion, you will decide to be a part of it anymore. Certainly it is easier for you to ignore the bad parts of your religion while you are young and don't have as much life experience. But the truth is, people get hurt, sometimes to the point of suicide."
(explain all the hurt that happens to people who get baptised into this religion, and why you don't believe any of it is necessary)
IOW, be firm and friendly. Speak to her with respect for her intelligence, but don't allow room for her brainwashing to discount your own intelligence and life experience, not to mention fatherhood. Force her to accept a father who believes her religion is hogwash, and wants her to know why.
Don't forget to get her involved, and keep her involved in lots of life building extracuricular activity.
I wouldn't hesitate to be a momma bear to the Elders, but keep your frustration with them totally out of your relationship with your daughter. Keep a sense of humor about yourself when interacting with her. Likely, the society would back off totally if threatened with a lawsuit on this matter. This is exactly the type of thing they don't want exposure on.
Your wife should also be able to accept this. Many witnesses do not get baptised before 18.
ps. just read about your daughter "tearing up" when you try to have a rational discussion. It's just another opportunity to show you care, and simply ask "what is making you cry, dear?" Convince her that you want nothing less than the best life can offer for her.