To not want to punish DD during my custody time?

And what would you have done in this scenario?

Only agree to punish/inact consequences instantly.
If DD does the crime then she does the time both with Dad.

Your DD is naughty not to get dressed.
That is a reasonable request and should need no discussion.
It's fine that her father parents in a more direct manner. Classrooms full of seven year olds are directed what to do every day.
A consequence would have been to travel to the party in her PJs. She then could have dressed in the car upon arrival because children can not be left in cars alone.

Discuss and agree with ex what is reasonable behaviour.
At seven she doesn't need micromanaging. She can dress, bathe, brush her teeth, read her reader, etc. and also use please and thank you, wait her turn, use table manners, be kind and listen to what she is asked to do - and do it.

Discuss, brain storm and make a list of acceptable and logical consequences such as ...
favourite toy up on fridge immediately, going to party in PJs, no sweets if vegies are not tasted, no TV tomorrow if can't leave screen and come to dinner etc.
Don't threaten anything that can not be carried out or is completely unrelated or is cruel or unequal to the crime..

Reward naturally with logical consequences too. An extra scoop of icecream, two books tonight, a new hair tie once dressed, giving her a responsible task like washing the dog, phoning Granny, positive feedback and compliments.

Remind DD that her Dad's house will be a little bit different and that is okay.

It sounds like you negotiate a lot with your DD - letting her choose rewards, explaining why, talking things through, even coming up with extreme measures like letting her go out in pyjamas and taking a bag of clothes if she doesn’t want to get dressed. You give her a lot of control in a way that clearly works for you both in your house. You’re raising her to be curious and feel like she has equal say in decisions that impact her, which is a great thing, when it works.

But it’s a style that isn’t always available and she needs to learn that when an adult tells her to do something, she does it.

Does she get in trouble at school for talking back?

It sounds to me like you have good consistent rules on behaviour. I would tell your ex that you won't be punishing her for things she did with him because you weren't there to see what happened and you have observed him being inconsistent previously. Stay out of the gymnastics issue, that's up to him as he pays for it.
If a grown man can't get a 7-year-old to put her clothes on, he is clearly doing something wrong. As you say, taking her out in PJs would have been a punishment in itself. Possibly he didn't really want to go to the birthday?

It's not hard to spot who is the better and most consistent parent here OP! Just the fact your ex isn't willing to work together with you on this issue shows that he could be a better dad.

I don't think you should punish her for behaviour at dads. If he's precious about you commenting on his parenting when you're just trying to help create consistency and help with the issues then he gets no say on punishment from you.

Honestly do not quiz her too much. It is bad enough that she is having to find ways of negotiating this shared parenting (which is none of her making) without stuff spilling over from one to the other. If she does something amiss on one place she should not have to endure being quizzed about it in both. Being piggy-in-the-middle is agony for anyone, let alone a child.

You do you - and if he decides to withdraw an activity that is in "his" time as a punishment there is not much you can do.

It sounds as though you have found a comfortable way of living with your DD and that she feels content with that side of things. But I do not think it is down to you to be asking her about actions when she is out of your orbit as it might feel just a bit too much for her.

However, there does need to be a way that you can organise a private conversation with your ex to achieve some consistency around sanctions and rules. But this should not involve talking with your DD about what happens at his place - just too much for such a small person to deal with.

If she does not like it at either place there will come a point as she grows when she just puts her foot down and refuses to go and, short of manhandling her, there is not a lot you can do.

She is in an impossible situation.

I strongly suspect that he’s not dealing with it well and then expecting you to do the parenting heavy lifting.

I’d send him something in writing saying that of course you’ll work co-operatively but he is not to seek to impose sanctions which you have to enforce without discussing it with you first.

As others have said, why didn’t he just stick some clothes in a bag and she’d have got changed once they got there? Or missing the occasion would have been the punishment.

It’s also not your job to steer him through parenting. If he doesn’t know to pick his battles and that consequences should be immediate he needs to read some books or go on a course.

You can't be his enforcer - nip that in the bud now. Otherwise what message is that sending? Dad is a wet lettuce who has to call for backup in the form of Mum to impose his consequences for him. Long term that will only be undermining his authority more!

This

I havent read the thread, its not ok to punish a week later, the punishment needs to happen at the time of the transgression and ideally involve both of you at the time, even if the parent who hasnt got care of her at the time also speaks to her so that there is a joint message from both parents, jointly parenting her

Its impossible to say if she is 'acting up' for him becuase he does put the boundaies in and you dont, or whether he is too inconsistent and unpredictable so of course she doesnt understand the boundaries

Why dont you source the online parenting courses for managing behaviour/understanding developmental stages and do them together, they're only short each session so you can spend 20 mins doing them and reviewing together how its put into practice with your daughter.

Exactly.

Having to co parent with someone who has inconsistent rules themselves is very difficult, and it’s very hard for the child.

Children actually cope quite well with different rules for different houses - for example my exh has a “shoes off” house, and I don’t mind if shoes are kept on downstairs (although I usually wear indoor shoes myself).

What they don’t cope with is a parent who blows hot and cold, and sometimes thinks things are funny but sometimes comes down hard. You need to be internally consistent.

No. He needs to parent her himself. Not getting dressed isn't even a punishment situation, it's a FAFO situation. She'd go as she was and her cousins would laugh at her and she'd learn from it.

He sounds ridiculous, and I agree with a pp that he could do with parenting classes. Ridiculous in the first place he let a 7 yo make him miss his Mum’s birthday- he should have dressed her or taken her in pjs with clothes in a bag if things were as he said.

Do you suspect that his version of events is not true? Your update implies this. Is he doing it out of spite in some way? Not jumping to that conclusion but you seemed to imply that.

No, he doesn’t get to impose sanctions on your time, especially ones that involve other people and you, and you definitely don’t need to follow through for him.

Any consequences he puts in place should be immediately or very soon after the event. Not a week later ffs

My other rule is no consequences that inconvenience other people (save for perhaps the person giving the consequences if they decide so)

Your poor daughter - having to cope with two households, two sets of rules. It must be exhausting for a 7 year old.

Agree; letting her leave the house in pyjamas and taking clothes in a bag is a very weird suggestion OP. Have you allowed that before?

Haven't we all dealt with a stroppy 6 year old who doesn't want to get dressed? Pretty standard behaviour in my experience. There's obviously a problem with how he's dealing with it. I find this with my DH, he's far too soft until he suddenly isn't and he'll go from 0-100 in about 5 seconds which then just escalates the situation and makes things 10x worse. You've got to have patience but also be firm and consistent when dealing with 6 year olds and it really sounds like he's not dealing with it well.

Totally unreasonable for him to try and impose sanctions at your house.

It’s perfectly reasonable not to carry a punishment forward in this situation. I do have friends whose children are over who will have their phone or internet taken away and both parents will stick to it or not allowed out for two weeks . But this is different and your child is younger .
your ex would like he needs parenting advice . Missing my mums birthday because my child disk t want to get dressed would not be an option . Children need boundaries.

He needed to get her changed because that's a normal thing people do before leaving the house. Questioning why she had to get dressed (a basic thing) isn't right here... the question is why was she refusing to get dressed?

Either she's pushing boundaries, or they are clashing.

That's a really nice system that seems to work with her. She responds to being able to choose to do something she likes and consequences involve the problem directly.

Does your ex have a more authoritarian parenting style? I can see why he's be upset at missing his mom's birthday meal, but if she did change from her pjs, what's going on? I would have taken her in what she was wearing personally, not missed an important meal.