Why is she now wanting to stop guitar and take piano? (She has been puttering around with our piano lately, playing songs by ear.) Since I am concerned about letting the interest in piano lapse, I have considered giving her lessons for both, but she already does karate, Girl Scouts, and baseball (which will end soon). How do I motivate my daughter to keep interested and practice on her own without nagging, yet not overload her? How much is too much?
As you have clearly articulated, those multiple interests and talents can lead to a very full schedule, which can overload not only the child but also the parent. Gifted children also need free time to unwind and to just "hang out," balanced with other times of high stimulation. Does your daughter's guitar teacher also teach piano? If so, you might be able to get him to integrate lessons across both instruments. If he is on a music faculty at a school or a local college, he may be able to identify a colleague who could help to coordinate lessons on both instruments.
Since baseball is ending, would it be possible to substitute the piano lessons for that sport? Since your daughter also takes karate, she will still be involved in a physical activity.
You can also sit and talk with your daughter about what her priorities are. If she wants to pursue multiple activities, ask her to choose a few to do now with a plan to switch to other activities in the spring or summer. Continue to monitor her for signs of overload. Is she cranky, unwilling to practice, or losing interest in one or more activities? If so, it may be time to pull back.
It's also quite reasonable to indicate to her that you need to pull back. If you have a job, other children, or other responsibilities, you need not feel guilty about setting limits on your daughter's activities.