Difficult DD

It sounds like she's acting out, but don't underestimate the impact that the smacking may still have, and it's clear that the pretend/play smack towards your granddaughter has really triggered some buried feelings.
There were 2 episodes of our parents smacking my sister and I that I vividly remember. A single smack each time with no more abusive features, but the anger and hurt that I feel has never fully gone away, even though we otherwise have a great relationship. The last time that I cried about it I was in my 20s, and if my mother joked about smacking my daughter I can imagine I may aggressively want to protect her from even joking about that.
I think apologising to her for smacking her as a child and the enduring impact it has clearly had on her would go a long way towards repairing the relationship.

You need to apologise for having smacked her as a child.

well if her childhood was so awful why is she relying on you for childcare. She can't have it both ways.

I feel for you OP, she sounds very hard work.

Memory is a funny thing. I have a sibling (who has always been a bit of a negative nelly tbh) who remembers all sorts of terrible incidents like that which either didn't happen or were insignificant enough to me that I've forgotten. I suspect it's total fabrication in honesty as our other siblings don't remember them happening either, but willing to accept this sibling genuinely believes these things happened.

Enid Blyton had two daughters, they had the same childhood and they remembered it VERY differently.

It may be that your daughter really does believe what she is saying in which case there is no point arguing over whether or not it happened or asking for an apology, as she will just think you are gaslighting her. You're probably feeling particularly protective of your late husband given that you cared for him so long and he's no longer here to give his side as you say. I'm so sorry for your loss, and for the hurt you must feel hearing ill of him from your DD after his death. But I think you need to let it go as trying to discuss it isn't going to end well for either of you.

You and your dd need a good chat. One where you listen, because it actually doesn't sound like you do here.

She has basically told you that she is traumatised by being smacked as a child, and you've shrugged your shoulders and then went out of your way to prove her wrong.

If you want a relationship with her and your grandchild you need to listen and accept what she says.

You have your perception, she has hers, and possibly somewhere in the middle is where the truth is. It depends on what you value more, being correct, or your dd and your dgc I suppose.

Were they happy when you moved closer? It sounds like your husband wasn't her Dad and she feels you've been focusing on him rather than supporting your daughter with her young family? If my mother turned up on my doorstep and started throwing her weight around I'd have issues too.

I feel for you. It sounds as thought your daughter has some emotional baggage that she is working through, and is taking it out on you. It is hurtful. If you can, try putting just a bit more distance between you. I don’t mean sulking, I just mean that you see less of her, while keeping the relationship positive and the childcare arrangement with the grandchild.
I wouldn’t be making any more plans like spa days etc. This is to remove you from the firing line. When you spend a lot of time together, she will take her emotions out on you, hurt you, and blame you for the fallout that ensues (and you might do the same with her, when emotions run high). If you don’t see her as much, there will be less opportunity for this to happen. She will need to find other outlets and ways to work through whatever she is processing, and you will have less hurt feelings to chew over. You can see more of each other if and when the time feels right. Absence makes the heart grow fonder, as they say.

Forget looking for an apology nobody responds well.to an ultimatum. Your dog remark may have come across as a criticism about it's care. Then you went and made a inappropriate remark about smacking. Really really inappropriate and surely you don't to be told that . And to deny her story about being smacked by her father is not right . Why would she lie ? You didn't have to defend him just maybe say I'm sorry that happened. I was smacked as a child but my parents in later life admitted that it was wrong and very widespread. I seem to be criticising you but just trying to show you a different side.

Helping them , spending time with your granddaughter should not have strings attached . Don't let a fairly non event ruin your relationship. Ask your daughter if you can both move on and start afresh .

You need to look to your own behaviour. You escalated the first incident from what sounds like her being a bit short with you to you asking her to leave your house. Then you involved her partner. When she told you your husband had smacked her you accuse her of lying and involve her brother. What do you think is going to happen?

See the thing if your dd was that traumatised by being smacked as a child why would she trust you with her child?

so all this 'being affected badly' business doesn't make sense to me.

I wouldn't leave my dd with someone who had hurt me as a child simple as that

she's got the hump over something else and you are the scapegoat for it I expect

Hmm.

What is considered good childcare changes.

These days smacking is (generally) considered inappropriate and there is a movement to make it illegal in England. Personally this isn't something I would joke about and I can see why your DD didn't like it.

Equally, you can't be 100% sure your DH didn't smack her as a child. You won't have been there all the times that she was with her dad and it's the sort of thing that you remember as a child whereas your DH might never have even mentioned it to you.

I wouldn't be giving you a heartfelt apology (or any apology to be honest).

Obviously your DD may well be very difficult in many ways and this is just one situations, so maybe you are more in the right most of the time.

But brutally she controls access to your grandchild. Either get on with her or get less access.

OP, I know that smacking was probably normal when you were a parent, but you have to understand that things have changed and it is massively frowned upon now. Whether or not your late DH ever smacked DD, you have admitted that you did. This may have affected your DD more than you realised at the time and may well still be upsetting for her now.

You say you're expecting a heartfelt apology. But I think you also need to consider giving one. Be the bigger person and apologise for your past mistakes.

She seemed to have been gearing up for a fight that day but maybe she remembers things differently to you? I sometimes say about things that happened to my mum and she doesn't think it happened and then we go to my sister who tells us she saw something entirely different to both of us! Definitely give her space and with the greatest of respect if someone told me I needed to apologise they'd rile me up twice as much. You both need to talk (and not be around each other so much)

It’s a fine line to tread being grandma .
I would give her a little space for now … then send neutral messages . I wouldn’t churn over this incident or the past unless she specifically raises it - purely because this all delays access with your grand daughter .