I am indeed against dancing in the modern sense of the practice. However, that does not mean I am against you. My conviction comes from putting together several biblical precepts and applying as best as I can to my life. Let me see if I can explain.
First, let's look at the good things about dancing. It is good exercise. It helps develop coordination. It works as a socializing tool (that is, it helps kids get to know each other and learn to react to one another). These are all good and dancing certainly provides them.
But now, let's look at the negatives about dancing. Dancing encourages seductive movements before the eyes of others. Our daughters are taught to wiggle in various ways in front of the boys. Also, most forms encourage physical contact between the sexes to varying degrees. The world would laugh at our concern over this, but as a parent I believe you can understand the dangers of encouraging this. Dancing also prepares the young for the greater "adventures" of the night club and other entertainment forms. In 1 Thessalonians 5:22, we are told, "Abstain from all appearance of evil." Dancing is often associated with evil in this world.
Traditionally, Baptists have opposed worldly activities such as dancing for the reasons given above and more. But today, even most Baptists have fallen away from these convictions. Neither you nor your daughter are evil because she goes to dancing school. However, I hope you will pray and seek the will of the Lord in this. Go to the Lord and tell Him that you are willing to do whatever He wants, ask Him to reveal His will to you in this, expect an answer, and then obey Him. I am sure that He will help you with this decision if you will be submissive to Him.
One final comment: The benefits that I admitted can come from dancing in the earlier paragraph can also be gotten in other ways without the problems. Families and children who love the Lord and practice strong convictions do not have to be miserable. We found that out with our own children. I believe that they had a very happy and exciting childhood and so can yours.