Sister angry I “yanked” my nephew’s arm and told him off

She said “how would you like it if I hit you in the face” = a suggestion that she might potentially hit him in the face. “If I did x, then..” literally how the English language works.
Of course she had no intention to actually hit him in the face (well presumably) but a 2 year old isn’t to know that .

Jesus Christ, that's not threatening to hit the kid!

If I was OP I'd take the dog and go out next time, I couldn't be bothered with the drama that appears to come with looking after the kid from two parents who can't be arsed.

I wrote:

”I don’t expect another adult to suggest to my 2 year old that they might hit them in the face.”

Thats exactly what OP did. She said “how would you like it if I hit you in the face”.

Nope. As I said, even if I am not in the room I don’t expect another adult to suggest to my 2 year old that they might hit them in the face. That is not ok whether I am in the room or not.

Do you always make things up? OP did not threaten to hit the kid FFS. That would have meant her saying something along the lines of 'I'll hit you in the face if you don't leave the dog alone'. As you're perfectly aware that's not the same as her saying 'how would you like it if I hit you in the face?'. Two totally different meanings.

But the dog was lying minding its own business when it was hit. What was op supposed to do? Know the future and put the dog in a different room?

And as I said, if you're not in the room you can't do much about it. Including knowing whether the tone, words etc were appropriate for the situation.

if you are not in the room you don't have a choice about how your child is corrected. The answer is to not leave the room, or to accept that you have hadned responsibility to other adults.

Nope. As I said, even if I am not in the room I don’t expect another adult to suggest to my 2 year old that they might hit them in the face. That is not ok whether I am in the room or not.

Yes, your BIL should clearly have been supervising your nephew but at the risk of stating the blindingly obvious, you also had a separate and stand-alone responsibility to supervise any possible interactions between a child and your dog. It’s your dog. You don’t just get to have a dog and expect other people to supervise all the potential interactions between the dog and children, without any involvement from you. Whether it’s in his own house with your nephew or in the park with children you’ve never met before, it is absolutely your responsibility to risk assess and make sure that there are no interactions that could lead him to snap at a child, especially bearing in mind that that child is 2 (not almost 3 at all) and will almost definitely behave unpredictably. It’s really quite something that you were laying hungover on the sofa not paying any attention to the potential interaction and then blamed a 2 year old for it?! Along with the tone of your responses on this thread, it’s not a huge surprise that your family are exasperated.

God forbid a mother take a break when her husband and sister are in the child’s presence

No parents get things wrong all the time but good parents don’t continue to defend their actions, they apologise for their mistakes.

She didn't threaten to hit him in the face. She posed a pretty standard rhetorical question to try and get the child to see things from the perspective of the dog. "How would you like it I took your yoghurt?" was something I said to my own toddler yesterday when she snatched another child's snack at a party. I am sure people on mumsnet are too literal for real-world interactions. But above this, if you are not in the room you don't have a choice about how your child is corrected. The answer is to not leave the room, or to accept that you have hadned responsibility to other adults.

Even if I’m not in the room, I don’t expect other adults to suggest to my 2 year old that they might hit them in the face. Or to accuse them of being “mean”.

You can call this “discipline” if you like, I call it a threat of physical violence, and a form of verbal abuse. It’ll be a hard no from me in any context.

Surely you’ve seen your sister’s parenting style?

Which appears to be chatting in another room while other people look after her kid.

You did, but you need to learn from us since you have a young nephew.

Who's the 'us' that the OP needs to learn from?

59% of voters think she was not being unreasonable.

Whilst OP was kneeling down for a gentle chat the dog could have bitten the kid! No doubt the parents would have then blamed OP for not pulling him away. It was a spur of the moment reaction to prevent something happening.

Knelt down for a gentle chat before removing him from next to the sofa within reach of the dog? Jesus H Christ, now I’ve heard everything.

You did, but you need to learn from us since you have a young nephew.

The child’s father was RIGHT THERE!
You should have stood between the child and the dog and taken the coaster out of the child’s hand. Then, if the father didn’t see what happened, you should have told him right there and then - xxxx just hit the dog with this coaster.

You should not speak to young children in anger, and certainly not other people’s young children.

I don't think you should have grabbed him, 2to3 is pretty little, he wasn't choosing to be unkind, so i think I'd have knelt down and looked him in the eye and explained dogs don't like that, especially when they're asleep lets stroke him together kindly. Although given your BiL was right there, I'd be more likely to have elbowed him and said "can you please watch your son because he just whacked the dog with a coaster"
Having said all that, she's being unreasonable, you don't have kids, you won't know the "best" way of parenting and his dad wasn't watching him. Your dog is old and very important to you, you didn't hit or shout (unless you did) and presumably you didn't hurt him with the arm hold or bruise/mark him at all (if he was hurt, totally different!) She should just have rung you and said that isn't how we parent, please don't do it again and sorry my husband wasn't actually watching his own child. When mine were toddlers we didn't really ever stop watching them when at someone's house, especially with animals or anything fragile - it's a recipe for an issue (mother of a dd who was a cat tail puller...!!) Demanding an apology is a bit childish of her.

Why do people think I should know all of Supernanny’s parenting tactics? I’m not a parent or childhood development specialist. I had a horrible situation forced upon me.

You overreacted massively. I don't care if your nephew is 2 or 12 you don't threaten to smack them in the face!
Telling him off is one thing but to be so OTT is quite worrying. I don't think I'd want my child around you even if you did apologize.
You should have just taken the coaster and said we don't throw things at or hit our animals, you must use your kind hands.
Did you actually give your BIL a chance to intervene or did you just march in and start telling the child off (and threatening them)? Also he snitched on you? You sound about 12 . Why was it a problem he told your sister unless you knew you'd overreacted