Emotional issue - is my child "normal"?

I'm at my wit's end with Miss M..

This morning she wouldn't let my brother out of the house to go to work (he leaves at 6am, and she kept following him down the drive, and kept doing it every time he'd bring her back inside and tell her she had to stay inside)... and then she stood in front of the door. Being that my brother's not the sharpest tool in the shed (he has learning difficulties, which also affects his maturity and reasoning), he didn't think to wake us up to deal with her, so he ended up being late for work. She's also been going into Master C and my brother's room and waking them up between 4 and 5am every morning for the past few weeks, no matter what we threaten or say.

Her teacher came and spoke to me at the end of school today, her and one of the twins in her class (a boy) were found missing at the start of class after recess... they were found hiding in the playground. They both got in trouble.
The teacher's also realised what I was talking about with Miss M last year, with her behavioural problems. They're coming out at school now instead of just at home.

My mums answer to this is that I should ease up on her at home, and stop being so strict. I don't see how that can work, because there's just so much silly stuff she does, like running from each end of the house to the other end and hitting the wall, and then going back and forth and back and forth and back and forth - or not sharing with her brother when the toys they're playing with are HIS, and not going to bed on time, blah blah blah. Usual kid stuff, but she fights me at every turn.

Her teacher is now seeing the misbehaving, not concentrating, not sitting still, not listening, and being defiant. It's kinda nice, because she can now see what I was talking about and that it wasn't all in my head. But on the flipside, it means it's NOT just me and there's something wrong with her.

Her teacher is going to find out what they can do about getting a behavioural specialist to come into the school and help her, or see if we have to go out of school hours or whatever.
It's been a rather stressful day, and I had to miss night class tonight because I couldn't leave her with my brother. I just didn't trust her to behave and not give him a hard time.

So... yeah. that's been my day in a nutshell. It's been a good one... not.

So after teachers and other parents telling me that my kid is either "naughty", "a bad kid" (yes, she's been called that by other parents before), or "a typical 6 year old" (she's a lot more extreme than that), it seems like someone in authority is finally seeing what I see every day.