I've messed up with 3 year old

Gave you talked her about the crying and how it won’t get her what she wants, but if she asks nicely and talks to mummy then you can try and resolve it, maybe she thinks this is the only way to get her way, the only way she knows how to communicate with you ? It’s just a thought.
I remember losing it when my son was three because he was tired and it was nap time, but he wanted to go out and the crying was non stop , I’m not proud of it but I shouted and I still now 14 years later remember raising my voice and wish I hadn’t.
Maybe this weekend try and talk to her and put some small rules in place.

Just to edit to say the brusque, redirect approach is when she's crying over stuff. Otherwise I think it's probably good to lower expectations a bit and show more love and attention. Have a bit of fun with her
Some kids are whingey. They'll grow out of it as long as there's clear expectations
Or they won't- some adults get moody over stuff 🤷

Its tough when you have a child who defies you at every point in the day but she isn't spoilt she is just a normal 3 year old, learning boundaries and becoming independent.

We are all guilty of not reacting in the best way at time when things get on top of us but it is how you learn and change that which is important.

Remember you are her safe space. She knows that she can exhibit anything she is feeling and you will still be there for you. She will always be perfectly behaved with nursery and grandparents as she doesn't know they if they will be there for her if she lets out some of her emotions. This really helped me to reframe how I was seeing the behaviour in my eldest and how to work with him.

Well I think you probably need to adopt a stoic, roll eyes and redirect approach
Of course thinking step or sitting out/removal of treats fine. But of course it is draining all day having a more whingey child. Did she even show any reaction to you losing it? Because if she didn't then you know for sure you need a different reaction as she is seeking attention. So cultivate more positive attention and ways for her to have some responsibility within the home so she can increase in confidence

Visible chart with sad and happy faces/expectations of house rules - for you all. Including you - no shouting or mummy has to have tele off time/go and calm down lol

More one on one time in her world so getting down on the floor to play undisturbed etc lots of roleplay with toys about how hitting/pushing is not ok, how to be a good friend. Dont bang on about it though as shes only 3.5.. its a difficult age.. reiterate its OK to cry when you don't get what you want but you can't follow me around crying or whinging. Do you want a hug? If she says no then say OK, I'll be here for a cuddle when you want it.

Have you considered additional needs?

girls in particular are very good at 'masking' so maybe this is what's happening at nursery. But she feels safe enough to 'lose it' at home, with you.

do some reading & see if her behaviour/masking fit.

have you tried love bombing her?

Maybe your DH and in-laws are right and you are on at her too much. All children are different and juts because naughty steps worked for you older ones doesn't mean it will work for all children. Maybe try a more gentle approach and pick your battles. If she is always being told off she is going to stay in the cycle of being angry and sad.

She cries when you get there bec you are her Mum, and she is trying to communicate things that have been troubling her through the day. To be honest it sounds like she's seeking support and connection with you and not getting what she needs- she needs you to be okay with her feelings, not tell her to cry somewhere else. Punishment like naughty step really doesn't work to change behavior, you need to guide and teach what you want her to do she's only 3.

We’ve all had moments when we react in a way we shouldn’t.
i remember my daughter screaming all the time at 3 and it’s so draining. I recall one day saying something like, I don’t like this screaming, you can scream in the hallway until you’re ready to use your words. She (and I) was surprised I really did put her in the hallway and shut the door and she came out a few minutes later very quiet - I’m not sure id recommend this approach, but I mean I can see why you said go and scream upstairs.

Shell be tired after nursery, the reality is you’ll get the tired and difficult bit of her day. Go knowing that and it’s easier. Making things lighter and funnier works, going heavy on punishments won’t - she’s too young and she needs you to show her how to regulate her emotions, otherwise she’ll just learn to loose her rag like mummy.

Imo she has too many main carers who aren't on the same page with expectations..
If gps aren't raising her in their time to your desires then she needs put in nursery. More routine maybe?

I feel for you - having a child that fights you on literally everything is soul destroying.

be kind to yourself you’re doing well that you don’t shout every day.

you’re trying to give her calm consistent boundaries and deal with her behaviour and nobody else is helping as they pander to her so you’re having to deal with it alone.

don’t give up, just look after yourself.

When she is with you, she feels safe and shows her emotion accordingly. She’s telling you she’s unhappy. You need to listen to her.
Misbehaving after nursery is normal, they’ve been inside listening to rules and conforming all day, they’ve explode when out like a pressure cooker.

Your poor daughter. It’s clear you don’t like her. She will know this. I grew up in this kind of environment. It’s extremely damaging. Maybe you could sit on the naughty step and think about your behaviour towards her.

And this is why we have the problems we do. Of course you can give small children age appropriate consequences for bad actions. I think you should go and read the thread about the trend in MC privileged kids and trans identity.

Just ignore her crying and guide her to do what she's being told to do. She needs boundaries and consequences.

But of course, this is in addition to warm, consistent, affectionate care from loving parents.

I can't find it in me to be kind I don't think. I feel really sad for your DD. I don't believe in naughty step or punishments for small children, or shouting for that matter. She's 3 for goodness sake and her behaviour is a response to how you treat her in my opinion.
You expect her to behave in an ordered way for your convenience but she doesn't understand your world, at 3 she just doesn't have the capacity for that.
What she would respond to is kindness, explanation in simple terms and making tasks fun.