I don't see how this is an "impossible" conversation that has to be a huge source of drama. My kid and I had it when she was six or seven years old.
Tinker Bell: Mommy, I am a big kid now. It embarrasses me when you walk me in to the gym and piano lessons and stuff. It also distracts me when you watch. Can you drop me off in the parking lot and wait for me out there at the end of practice too?
Mommy: If you show me that you can walk through the parking lot safely, I will drop you off in the parking lot near the door. I need to come inside to pick you up, though, because the gym requires it, and because you are incredibly slow in packing up.
Tinker Bell: Okay.
Simple, respectful, open conversation on both sides. She explained what she wanted and why, I explained what I could and could not do and why. In the end, I was the parent and made the rules, taking her needs and preferences into consideration. Not an impossible conversation at all. Conversations like this are a natural and important part of parenting, and of growing up.