Children usually act out with their primary caregiver, it's a sign they trust them. So they hold everything in from the day and when mom is there, explode! This is normal.
I think you're stretched thin, and it's adding to your stress and anxiety, which is adding to hers. You don't mention a partner, are you a single mom? If you are a single mom, something that might help is hiring a helper in the mornings. I'm a single mom and this is not something I could afford, but it would have changed my life. If you have a partner, having them help you in the mornings will reduce stress for all.
Be proactive. If you hate being late in the morning, maybe get everything ready the night before and wake up 30 mins earlier for some alone time. When you're with your daughter, do you give her enough face time and cuddles? Give her undivided attention before the day starts. If she keeps hating daycare, mayeb there's something there?