If she's so well behaved otherwise, and even takes discipline acceptingly as you note, then I'd sit down with your husband (and not her) and think very hard and make notes on these kinds of things:
When do these tantrums occur? Time of day; event that's happening or about to happen; what stage she's in, if she's in the process of getting ready to go somewhere or leave somewhere; etc.
Does she have the tantrums at the neighbor's or at school when she is arriving at these places? Or when she has to leave and doesn't want to? Or when she's in the middle of the time there and is thwarted in something she wants -- told "no" about something?
Does she have more of these in the mornings? Midday? Evenings?
For the tantrums at school, do they occur at the same general time and place? When she's being dropped off? Do they occur in front of the same general group of kids, or the same teachers, who witness them each time?
These kinds of questions could help you see any patterns. She might have trouble leaving situations where she wants to stay (dinner at the neighbor's is over but she won't leave, for instance) or going in and starting new situations (she arrives at school but doesn't want to go in and would rather go home). She might do it at times when she feels she does not have your full attention: When you are getting yourself ready for work, when you are about to leave her at school, when you are chatting with the neighbors.
You can work with her on giving her LOTS of advance warning about "We're going to leave in 30 minutes -- the amount of time it will take you to play one more game of cards with your friend" then "We're going to leave in 10 minutes -- right after you pick up the cards" etc. (Don't just use times, they mean little to her at this age, but associate them with how long it takes her to do X). Same in reverse for starting things/new situations. "We're going to leave for school in 15 minutes, the time it takes you to...." Even possibly use a timer if she doesn't freak out at timers -- some kids love them, others hate them and it makes things worse.
Yes, the eating and sleeping are probably factors in all this. She may be hungrier than you realize in the a.m. when she's screaming for you to do her hair; be sure she eats before the getting ready, and give her a healthy "second breakfast" in the car on the way to school (cheese stick, whole wheat crackers, dry Cheerios mixed with raisins, etc.) and see if that distracts her while also staving off tantrums as she arrives at school. You said you don't see a connection between eatiing and the tantrums, but remember, the "blood sugar crash" that makes many kids go into tantrums doesn't occur for a while after eating; she may seem fine and then suddenly crash out and get a bad attitude. Same with sleep --she may seem able to wake fine in the a.m. when she is tired again by the time she's in the car on the way to school. (School arrival tantrums in particular may be connected to needing more sleep and more food first thing.)
Also, are there any changes this year? Is she in K for the first time so that's a change? She might be pushing her boundaries to see if you'll let her not go, if she thinks she dislikes it. If she's going to a preschool or day care she's been used to, that may be less of a factor. If you've only recently gone back to work so that's new for her, she may be pushing your buttons because she doesn't like the situation. Examine those things too. You can't change the work/school situation but you can give her more sleep, more food and a very set routine so she knows what to expect.
As for screamiing -- Don't hear her if she screams. She wouldn't do it unless it got her some form of reaction or satisfaction; she thinks it works, somehow, even if you think you aren't reacting to it -- she thinks you are. Try telling her, calmly and when SHE is calm, that the new rule is: Using outside screaming voices indoors means no one can hear her any more. Walk away from her when she screams and ignore her completely until she can lower her voice. This may take some time and end up with her screaming louder and louder and finally in tears because "I KNOW you can hear me, mommy!" but you may need to really stick to your guns.
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