I've got a 6 and 3 year old daughters. The 6 year old can be very strong willed, but she's never out of hand and is always contrite when told off - but kids do anything to seek attention, yet don't always distinguish between good and bad attention.

Your wife shouting, and you imposing harsh penalties are big displays of attention. You're effectively feeding her craving, and you will make it worse.

In my experience when punishment doesn't work, turn it into a reward. Have a big chat and find out what 3 things she really wants, and say she can have those 3 things if she's good at school for 3 weeks.

There's definitely more going on than her being naughty because she's a bad girl. How much time do you spend with her? How often do you do family things together? How much do you praise her for good behaviour?

Finally (and not directed at OP) Anyone who thinks kids can be taught with violence doesn't deserve to have children.