another vote for autism.
try ear defenders at tea time. or eating separately before everyone else.
try stepping in before she gets overwhelmed. (when she starts to get arsey is the warning sign) firm pressure, rocking in one direction, weighted blanket (dd likes the wheat bags) firm massage. food.
you and dp need to get consistent. Go on a parenting course. It might solve the issue, if not then you can say you are doing xyand z but she still has diffiulties.
I removed computer time for mine when he misbehaved, was beginning to get towards meltdown, but he could earn it back by calming down.
there are signs of autism other than the behaviour. the sensory issues, (tickling, )
sensory seeking (thumb sucking)
talking in a babyish voice
social difficulties with lack of friends until recently.
Does she have any other sensory issues? (leans on you, lots of jumping off things, doesnt like noise but makes noise when it is noisy, doesn't like labels in clothes, fussy about socks, likes watching spinning things, rocks, licks things, chews on clothing, sniffs things or hates the smell of certain things,) look for over or undersensitivty.
does she get jokes, sarcasm, inference? is she literal in what she does. (and probably gets into trouble for it?)
how does she behave in the supermarket?
(she may be sensory seeking with the door slamming)
has she any special interests? Might appear less unusual than those seen in boys.
how does she play with toys?
does she seem more immature than her peers?