JOEL - It is very nice that you are considering to allow your daughter to join the LDS Church. I have a 17 year old daughter and it is very comforting for me to know that she associates with other young men and women who share the same ideals and standards as we do in our church. I am sure you feel the same about the Seventh Day Adventist(SDA) church.
If you are uncomfortable having the missionaries in your home the best thing for them to do is to meet with your daughter in another LDS member's home. Your idea of the library or some other public place could work, but the spiritual atmosphere might be better in someone's home.
As long as your daughter is under 18 years of age she would first have to have your permission to be baptized into the LDS church if she so chooses. The Church recognizes and respects the wishes and authority of every parent of every underage child no matter what religion they belong to. After she is baptized there will be home teachers assigned to her. Although they would much rather visit her in your home, arrangements could be made to visit with her at church or in someone elses home. Since your church meetings are on Saturday and the LDS meets on Sunday, logistically there would be no problem for her attending both churches. Our church has no restrictions about members occaisionally visiting the services of other faiths. However, when your daughter is baptized she makes a covenant or promise with God that she will try to learn and live all the doctrines and commandments associated with the LDS Church, which in some cases may conflict with the teachings of the SDA. This might tend to be a little confusing for someone at her age and level of maturity. And if she does become a member of the LDS church, how would she be treated by the members of the SDA if she continues to go there as well? It is also important for you to support her decision to be baptized even if you are not interested in the Church. If you cannot support her in her decision and insist that she attends your church as well, her future LDS Bishop might decide it would be better for her to wait until she is over 18 years and on her own before she is baptized. She could still attend our church meetings on Sunday and associate with her friends there and also go with you to your church on Saturday.
I don't know the type of relationship you have with your daughter and I don't know your daughter, so it is difficult to tell you what is best. You are her parents and as such are responsible for her happiness and well being. As her parent it would be very important for you to talk with the missionaries and her future Bishop about your concerns. They would then be able to tell you what is the best thing to do. They will not try to talk you into doing anything that is not in the best interest for your child.