I would... make your ENTIRE routine, at night, MUCH earlier...
She seems real over-tired... over-tired kids actually cannot sleep, have a harder time falling asleep, and wake more... and get more "hyper."
For me, for example: I would, start her whole bedtime routine... 1 hour earlier. Having her show end at 8:15... is late... then everything after that... is later... then it just gets all later like dominoes.
And it is too late... for a 3 year old.
I have 2 kids... 4 and almost 8. I start, WINDING-down my kids, 1 hour... PRIOR to their actual bedtime.
Kids need to wind-down first... not doing it AT bedtime... but prior. It is "prepping" the child for bed... time.
Before bed, I make everything quiet, dark and leave only 1 lamp on... they brush teeth, put on pajamas... they can watch Little Bear or something, or do something quiet.. then it is put away... and go to bed. They do so. Without battle.
For them and me, it is the SAME EXACT routine... every single night. In the same order.. and wind-down, is ALWAYS in the SAME room. So, my kids get into the routine, like auto-pilot.
Again, I really think, your girl is WAY over-tired... thus she can't sleep... thus she does not sleep... thus she gets sleep deprived again... thus she can't sleep and gets more "hyper" the more tired she gets and over-stimulated... thus she can't sleep, and it just all exacerbates itself, like a vicious cycle, and like a bad dream, for you.
There is also something called "Hyland's Calms Forte- for kids." Which, is all natural, not a 'sleep' aide, and not habit forming... but simply helps to calm a child. There is also something called "Animal Parade- Warm Milk" which is also for kids, to help them sleep. It being all natural and like "milk." You can try these... just so that she gets her sleep rhythms, back to normalcy. My friends have used it for when they travel.. and I have used it when my kids are sick and uncomfortable and cannot sleep.
These are NOT 'drugs"... it is homeopathic.
You can find it at Whole Foods or any natural food store, or online like at Amazon and read the reviews there.
I might also wonder... what does she eat at Daycare???? Anything with caffeine? Chocolate? Sugar? junk food??? Some of these things... affects kids a ton... even the littlest amounts....
All the best,