I disagree with SENORITA, this behaviour is perfectly normal for some 3.8 year olds. Some children are naturally defiant and love to 'break the rules' And the more they get away with the behaviour and the more they see you loose control, the worse it becomes. If the nursery haven't flagged up anything that causes them concern, I would say it is normal for your child- and you need to 'train' her for it to not be normal!
I have one of these types, she loves a drama, she is contrary and stubborn and has done exactly what your DD did yesterday. I carry a pair of baby reins on the pushchair. When she is up to her tricks I warn her I will put the BABY reins on her - if she continues to misbehave, I manhandle the screaming bansehee into the reins and drag her where I want to go, if she decides not to walk! I ignore everyone around me and march her straight home to the naughty step! she refused to walk with me 2 weeks ago and i did this in tesco and for the 20 min walk home, she screamed all the way. However, now she has that as a point of reference, the threat of me strapping on the reins is fresh enough in her memory and so she has only got up to the point of me warning her I will put the baby reins on, and she has complied ..so far.
She also loves to not get dressed in the mornings ( I have 6 kids to get out of the house by 8.30) I tell her if she refuses to get dressed I will take her in her PJ's and with no shoes on, and to prove I am serious, I take her out of the back door ( earlier than the school run) and pretend we are leaving, once her feet get cold and she thinks i will take her on the school run in her vest and knickers, she decides to change her mind.
Sticker and reward charts don't work so well with my one - ( they worked with my others) she loves to break rules, and hates to comply.
I would say that getting someone else( ie your husband) to deal with her is a fatal mistake- you have shown her that she has power over you and she is control. Remember that you are in charge, you are bigger than her, you are physically stronger than her. And she needs to know that she can rely on you to be able to help her when she is losing control.
Often children like this , for all their bravado are actually sensitive and are scared by their emotions. They don't know how to control themselves, it is up to you to make the rules, she can choose certain things( ie what to have on her toast- what colour shoes to wear) , but she needs to know, when you want to walk the right way through town, then whether she is doing it nicely, or screaming like a banshee- you are the one to be in charge. Life with a child like this can be a constant battle- but you will have to fight this battle if you don't want it to get worse.
I am not talking about breaking the spirit of a child like this ( impossible anyway) Being strong-willed and defiant can be marvelous qualities, but what i am saying is that ultimately your child needs to know she can trust you to be in charge- as it is too overwhelming for a child to have too much power.
For advice on the sorts of things you can do- and in general it is the always be consitent rule that is the main key to sucess- then go to your local parent center. Many of them have family liason advisers and parent craft type courses.
It can be hard having a child like this - mine is very draining, but I also LOVE her for her spirit, my others are fairly placid and easy going and certainly would never be defiant or knowingly do something naughty , just for a reaction. but my little 3year old rule breaker is a feisty little thing, and I hope that as she gets older, this will take her far, rather than be the annoyance that it is to me now. Good luck