How to stop DD embarrassing me?

regarding the hitting - if you can anticipate when this is likely to occur you threaten the punishment if she does it - take away whatever is importantly to her and follow through.
For the trolley incident for example, I would potentially let mine push but clear warning that if they push it into anything or anyone then I take over. And stick to it.
If I explain the reason I’m making a decision my kids are generally fine (I’m pushing the trolley because you will crash it etc)

By listening. Multiple people have already told you she shows all the classic signs of being ND but you just don't seem to want to hear it. You don't seem to understand that ND girls CAN regulate the meltdowns in school but only have meltdowns in a safe environment outside school. Just because in your mind she wouldn't be able to control it in school either doesn't make you right. Start listening to what her behaviour is telling you and stop burying your head in the sand.

You need to act right away when this totally unacceptable behaviour occurs. Speaking in a very firm cross voice. Not in a nicey nicey way. No darling we must be kind. Extreme disapproval must be shown and immediately taken home.

Lock her items off the internet.

Tell her if she throws it, she will never get another. Every time she misbehaves you will block it till the next day. So she can consider her actions...
Trolley. Tell her either she let's you, or you will walk out of the shop and stop shopping and DO it.
Tell her hitting is not allowed. Ask her what she things should happen if she does...

I totally agree. If you don't nip this in the bud it will only get worse. Also, she's only going to get bigger. She punching you at 8 she could really hurt you when she's older.

I do something called smiling minds with my 2. It's a free mindfulness / meditation app. It's worth looking at to help her with self regulation. Obviously, at a chilled time and not when she's kicking off.

For the shopping trolley example, I would say after she shouted once that I would be pushing the trolley if that happened again, then if it happened again I would be pushing the trolley and ignoring her tantrum even if it means standing next to her while she rages in a supermarket. I wonder if the problem here might be that you are embarrassed by her behavior when things don't go her way so you avoid the confrontation involved in setting boundaries?

If she hits her brother, she can't then play with him or near him, you give him lots of attention and she gets some time to reflect, then needs to apologize to him to be allowed to join in again.

Don't be embarrassed by her kicking off, your job is to make her into a functioning adult who can handle dissapointment and frustration and understands appropriat behavior, consistenly enforcing boundaries is part of that

This sounds exactly like my daughter who has recently been diagnosed with ADHD and Autism. You may find having a look at The Explosive Child by Ross Greene useful.

This is your problem. You’re pandering to her to avoid embarrassment and she knows it. She knows that all she has to do is kick up a fuss and you will give her what she wants. She is walking all over you because she thinks she can. Explain to her what you expect from her before you leave the house. Never allow your daughter to speak down to you in public, leave the trolley take her back to the car and explain to her that you’s are going to go back in but that you expect her to behave and if not yous are going home. If she starts again take her home. This is only going to get worse if you don’t stand up to her now.

What did that teach her? She was rude and shouted at you and you let her have her way because you didn't want to be embarrassed.
I would have taken her out of Tesco's if she was behaving like that. Also, who cares if she has a meltdown?

Do you give her the talk before you go places?
I tell mine we are going to x. When we are at x you will have kind hand, play nicely, listen. If you don't the consequences will be ABC. They know the expectations.

So why isn’t it ok for a teacher to hit back but it is a parent? What’s the difference in why it’s wrong?

Same. My nearly 8 year old DS would react like this and he has adhd.
ADHD is very well masked in girls (I know from experience; I was only diagnosed at age 39).

How often do you give in to save face in public or for the sake of a quiet life? If you sometimes give in and sometimes punish, you are not being consistent. There have to be immediate consequences EVERY time for her to start to realise you mean what you say. So for example in the supermarket, if she doesn't behave, you leave immediately. Therefore the consequence is there's no nice food that she likes in the house because you weren't able to get the shopping. Yes it's inconvenient for you but it gives a very clear message. I'd do the same in the park - if you don't behave, we're leaving now. Why do you think your family think she's spoilt? Is it because they see you giving in to her demands?

I'd recommend that you read 'The Explosive Child's such a sensible, helpful book that will really help to reframe your thinking.

What is your relationship like with your own mother?
Does your mother keep telling you that she is spoilt and it's your fault?

Because you seem more worried about how her behavior reflects on you as a parent, than the fact that your 8 year old behaves like a much younger child and seems to be competing with you like a sibling.

That might happen if there is a controlling granny living nearby who is everyone's mother so to speak.

I could be way off, but there's a lot of 'you are not the boss of me' going on, because your DD might be seeing someone else putting you down and taking your authority in front of her.

Oh ffs.

What sen does your child have? It sounds like you are very poorly educated about all of this. Hopefully nothing behavioural.

My oldest son is autistic and went to a special school. He was never any trouble at school but saved any meltdowns for home. This is very common behaviour for ND children. They have been using all their energy to fit in at school as best they can but then need a release and home is very often the safety valve. This is even more common with girls, who tend to be much more adept at making. In addition to this, girls on the spectrum are still very often missed as their behaviour presents very differently from that of boys. You obviously have concerns that this may be a possibility as you have spoken to the school. Perhaps you could keep a record of incidents with triggers behind them if possible. If you think there is a chance that she may have ASD, would you be able to afford a private assessment?

Absolutely.

I mean... We've even had someone suggesting beating a child who hits out.

Do you know what that would teach my ND children?

That is ok to hit because mummy did. Or, it teaches them to be afraid of me. I don't want my children to be afraid of me. It's my job to teach them how to manage their emotions. How can i do that and model that to them if i can't manage my own?

When one thump doesn't work anymore, do you wallop them twice? What about when that doesn't work? Three thumps? A black eye? What about if your child gets bigger than you and you've taught them it's ok to hit and they turn on you and repay you for all the times you hit them?

Someone speaks sense!

Why do you think they tell you that? What do you or another adult do to spoil her?

Try the books 10 Days to a Less Defiant Child and The Explosive Child. Excellent tips in both.

It is not unusual for a dysregulated child to hit, especially a less mature ND one.

There is a taboo around discussing it, but it really isn't that unusual in 7-10 year old ND girls. I participated in a research study on it (University of Durham, if anyone's interested).

Unfortunately it’s the same every time … us ND parents are made to feel like inadequate failures because our children have meltdowns and hit out.

These threads are teeming with people who think all issues can be solved by switching the WiFi off

NT parents hectoring ND parents, with ableist bullshit .. it’s tedious

Children know they can slap teachers and get alway with it.

they know a teacher is not going to hit them back.

thats why they do it, children know who they can hit and who they can’t.

same with the OP, she said her daughter only does it to her, no one else.

why is that I wonder? And don’t say some crap about because mum makes her feel safe🙄

it’s because she knows it’s ok to smack mum.

sounds like she kicks off/ hits out when she doesn’t get what she wants

leaving the playground
pushing the shopping trolley

She needs to learn life isn’t centred on her always getting what she wants.

So next time she asks for something don’t give it automatically, do a deal. Can she go to the playground…yes if she tidies her room and promises when it’s time to go she must leave without a fuss. Remind her when you get there. That way she will feel like she’s earned it and give it more worth. Equally if she then kicks off at the playground the consequences should be to not go next time.

She also sounds like she takes advantage of you. Hitting you and demanding the trolley indicates a lack of respect. I wonder if you give in too much and don’t follow through with punishments.
You need to build on your parent / child relationship. ie remind her you are in charge but also that you are there for her.

Op, please don't physically abuse your child as advised here.

None of this is any evidence that she's not ND. Also the trolley pushing is a desire to be in control which is a huge part of some traits of ASD.