Welcome to the fastpitch community! If you read this forum on a regular basis, you'll find many varied opinions about what is the "right" or "wrong" thing to do. One thing is for sure though. Every kid is different. Different ability, desires and goals.
As a parent, don't get caught up in what YOU want - let your daughter decide what SHE wants. Your role is to be the "guidance counselor". Let her make her own successes - and her own mistakes. This is IMO, the hardest concept to grasp for parents of athletic kids. You have to be very tuned-in to your DD. Sometimes at young ages you have to push her to "do her wrist snaps", or drills, etc. That's not her being lazy, but just being a kid. Now when she's 16 and you find yourself having to plead with her to practice, that's a red flag.
Most things are a common sense approach. If after 3 or 4 lessons she keeps telling you she doesn't like a coach or instructor, listen to her. Just because 20 other people think a particular instructor is great doesn't mean they are the right fit for your daughter!
Have fun and enjoy every moment of your "trip" with your daughter. It goes by much faster than you think!