Dear Kellie,
I think letting her give up after only one lesson would be a mistake. I'll bet at 7, she figured after one lesson she should be playing like Mozart by now. The very beginning is really kind of boring, but you have to learn the keys, finger placement, and how to read the notes. You really have to start at the beginning. I would let her watch people who've spent their lives practicing to get as good as they are. It might help motivate her. I never had a problem with my kids wanting to practice (to my dismay somedays). My daughter also studied the flute and for some reason, the piano was much easier on my eardrums. Speaking of drums, my son started percussion in the 4th grade and that kid was banging on every piece of furniture in the house. The piano, on the other hand, is so lovely and stationary and can't be dragged from room to room.
My daughter liked me recording her while she practiced. My son was just a baby and I'd put him in the high chair and she would "play" for him. She also liked practicing and playing for Grandpa.
Our piano teacher was at least 163 years old and it took her longer getting up the steps to the house than the lesson lasted. But dang, she could play the piano. She brought us all these really old pictures of her and her husband. They made their living playing in nightclubs and things every night when they were younger. She was a very interesting person so that was part of what we enjoyed about the lessons.
I don't think you should "force" your daughter about the lessons and practicing, but it just seems too early and a shame to give up after not even really getting started. I'd try to get her to stick with it. I believe she'll be glad she did.
Best wishes!
P.S. I also wanted to say that I know a kid who began music lessons at a very early age. That kid can play anything and even has his own band. They just went to Sacramento and recorded a CD. He went straight from high school to Humboldt State University and is majoring in music. He wants to be a music professor and at 19, he is well on his way. Your daughter may never be that interested in all the theory and technical aspects, but she may learn to love it.