As she is your 4th I expect you have tried lots of different tricks, I won't fob you off with "She'd clearly rather be up and doing something than wasting her time sleeping, I am sure she loves to learn!" I'll just mention a couple so hope I don't offend if you already looked into these.
I was wondering about night terrors but by the sound of it she is awake and agitated so maybe it's more like confusional arousal? DD's upset and sounds as if she's in pain or angry about something. She may not be completely awake, even if her eyes are open because part of the brain is still asleep while another part of the brain has woken up. So she kicks, screams, resists cuddling.
Don’t offer comfort or try to wake her up as this can make things worse. Let her tantrum. Just make sure she is safe and you're there when she needs you.
I know it sounds lame but try sticking to a routine, make sure she gets enough sleep and eliminate any overstimulating activities. Is she intent on keeping up with her older siblings?
Does she have a daytime nap still? Can you cut out the nap and put her to bed a little earlier. Try and let her avoid screen time for at least an hour before bedtime.
Is there a medical reason - ears, tonsils - some medicines can also cause confusional arousal including sedatives and antihistamines.
Does she have eczema or any sign of a food allergy? eg dairy, wheat intolerance.