3.5yo throws a fit when I pick her up from preschool because she doesn’t want to leave

This is her second week there and she’s never been in any kind of daycare before this. My husband and I have split care between the two of us coordinating our work schedules, and then my MIL has filled in on the days we both work.

She goes two days a week, and today was technically her third day, but every time I’ve come to get her, she’s irritated that I’m there.

She wants to keep playing. She’ll say “let me color one more picture,” or “let me shoot one more basket,” or “let me play one more instrument,” etc., so I’ll just be standing there awkwardly while the teacher is trying to make small talk with me.

When I finally force her to leave with me, she throws a huge fit tantrum, cries, yells things like “I don’t want to go with you!”

I’ve never heard of a child doing this. I got there at the same time as another mom today, and that mom’s child’s face lit up when she saw her mom, she said “mommy!” and ran over to her excitedly.

I expected my child to do that too.

My feelings are hurt. I’m trying not to let my daughter see that because I know it’s completely inappropriate for me to put that on her, but I feel so sad that she doesn’t want me after a whole day apart.

I’m also concerned about what the teachers are thinking. Surely this isn’t normal for a child to not want to leave with their parents, and I’m worried they think she doesn’t have a loving home.

Today she said she’d rather have her dad come pick her up instead (he cant; he works later than they’re open), and I asked her what the difference is, and she said “I love daddy. I don’t love you.”

I don’t know how to handle this. What’s going on? How do I deal with this? Has anyone ever even heard of this before?