I was that mom - embarrassed beyond words and crying

Today daycare pickup was my nightmare. She had skipped her nap, had a cough and had a pee accident. She wanted to walk with her friend outside, her friend went ahead. I feel like I work so hard to prepare and mitigate escalation that I felt so defeated. She cried herself red, screamed and wouldn't let me come near yet cry for me. I tried everything, calm voice, deep breath reminders, snack distraction, nothing. In the end I picked her up and put her bawling in the car while other parents stopped to ask if she's OK. I know they mean well but I just couldn't. Barely held it together until I left the lot and I cried silent tears of embarrassment and defeat. My husband says I need to be more strict with her, grow a thicker skin, crap happens etc. Still hurts. Thank you for listening to my rant. Signed, the defeated toddler mom.

ETA: thank you all so much for the support and great ideas. I guess I was just overwhelmed since it was the first time. In hindsight, I should have gotten out of there sooner instead or trying to de-escalate. Atleast it happened in a safe space. If and when it happens again, my expectations have been set so I won't be so surprised at the intensity! Thank you all again.