She sounds a little like DD in that after a sleep, she HAS to have a cuddle on my chest with her special pillow and both lovies too. If I end the cuddle too early for her, she gets very upset - I have to let her end it, though I can usually hurry it up a little if I make a suggestion about what she could do (eg. 'I see your favourite book over there. Why don't you go and read it?') rather than just put her down all of a sudden.
Honestly though, I love those moments with her and being slow to wake up myself, I know how it feels to be rushed in the process!
It's hard for young children to calm themselves once worked up - she probably really does need your help with this so she doesn't reach the retching stage. I have found getting down to their level and re-directing their attention to an interesting activity ('Is that a bug I see on the wall?' 'Oh, here's dolly and she needs to have a ride in the pram now' etc) can really help, and you don't have to give in to her tantrum, just take her mind off it.
It's a difficult time, and I think you're probably the odd one out if it's NOT happening to you at this age/stage! Hope you have a better day tomorrow.