Storytime too strict?

I’m curious as to how other’s libraries run their storytime and if I should wait until my 15 month old daughter is older to take her.

I recently signed up for story time at our local library once a week. The session is 20 minutes long and is free. My daughter is super head strong and knows what she wants, so I thought it could be a struggle for her, but I wanted her to interact with kids her age. They do a welcome song, read 2 books, do finger play and movement and a closing circle. They have a table in the back with crayons out for siblings. It is advised that those attending don’t stray from the story time carpet and try and participate. My daughter refuses to participate at the circle. Instead, she wants to sit in the chair with crayons and sing and do the clapping at the chair. She watches the others kids and instructor and is not a distraction whatsoever. Last week, the instructor seemed annoyed and kept asking I bring her over in front of everyone else. But when I tried, she’d start crying.

Are storytimes usually this strict? I don’t want to ruin others’ experience and I’m a teacher so I’m aware that there needs to be structure to planned activities, but I was a tad embarrassed last week.