Is this normal? AIBU to feel upset about this?

I definitely would be asking your step daughter is she ok with this.
I would be making it clear she does have a choice in all of this.
I would tell her it is ok to go along with this very strange and unusual behaviour from her mother if she wants to, but that it is ok to change her mind and not want to.

This is very controlling behaviour and not normal.
I think it is very important your step daughter knows it is not normal and she has choices.
In a normal household this would not be normal behaviour.
There is nothing wrong in calling out batshit behaviour.

Her mother sounds unhinged.

This is genuinely insane.

I don't think you are being unreasonable at all and I perhaps do think your DSD will feel a certain kind of way about this.

I experienced something similar but as a child. I lived with my mum full time and saw my dad probably 10 times a year (he moved to the other end of the country but used to drive up to visit me). He remarried and I would see his wife a couple of times a year. One year when I was around 10 my Dad took me away to Spain. My mum had packed for me but when I arrived my dad's new wife had bought me a new set of clothes which she'd brought with her and I wasn't allowed to wear the clothes I'd brought with me from home. It really upset me as a child and made me feel she was saying what I had with my mum wasn't good enough and she was embarrassed to be seen with me as I was. I'm not sure if sharing this will achieve anything but it may give an insight to your DSD's perspective, although it is a different situation.

Oh poor kid. She’s desperate for her feckless mother’s approval. I hope you and her Dad are able to make up for her shitty shallow mother.

13! Genuinely pleased look into getting some counselling or psychological support for your daughter if she's not already getting/had some. There is a lot she will need to process. Expert help on how to distance herself from her mother's approval would be valuable and protective.

Jeez she sounds nuts! Absolutely nothing to do with you OP - the woman obviously doesn't truly care about her daughter's upbringing as she isn't actually bringing her up so can't be that bothered. Sounds to me like she wants DSD as some kind of fancy accessory which is why she wants her to look a certain way when she takes her out.
Clearly way bigger issues linked to the court order here.

Reading your second post I am really glad your DSD is living with you and not her mother. For a parent to want to control what their 13 year old wears to the extent of picking their outfits for them? Take that desire for control into all areas of the child's life and what a horribly restrictive upbringing it would be.

Wow, what a piece of work she is! So she sees her daughter once in a blue moon and would rather waste time while she showers
OP, you're lovely. This woman isn't normal. She's throwing her weight around to hold onto the modicum of control she still has.

Your DSD sees her mother so infrequently that having the experience a positive one, I think, is important.
Tell your DSD that she is very well dressed and that her mother means well but is out of practice and nervous being a mother.
Ask your DSD how she feels about the visits?
Does she want to go?
Don't take anything personally. The mother doesn't cope like you do.
At some point you might need to teach your DSD to be kind but assertive about her own outings.

Why on earth are you twisting tto be about you? Sure sounds all messy but this is weird

I wouldn't take it as a dig at you but assume the 'mother' has some kind of fixation with cleanliness. It must be more hurtful for your DSD to have her mother imply she can't care for her basic hygiene adequately. I would have thought she could tell her mother 'I just showered and done my hair and teeth why do you need me to redo them?' in a polite tone without upsetting the apple cart too much. At least then she could find out exactly what her mother's issue is, and it is the mother's issue, not you or your DSD's.

Concentrate on the big picture. What does your stepdaughter need you to do, to limit the damage this is doing to her?

Whatever her mum might be implying about your parenting - even if she were correct which I'm sure she's not - is a tiny dinky dot next to the horrible message she is sending to stepdaughter, that she is disgusting, not good enough etc.

What? So we shouldn't be teaching kids boundaries when people are treating them like shit? How absurd!

God, how grim. How does DSD feel about seeing her mum this infrequently? I get you feeling offended but I don’t think this is a woman whose opinions on your parenting you should value. I think your questions need to be more about how do I protect DSD from the impact of her mum’s behaviours - which I can see you already are considering of course.

It sounds like the issue lies with her, not you or her daughter.

A terrible idea to teach a child she can say no? Sounds like a worse idea letting the child think thay have to pander to a dickheads demands.

I don't think it's anything to do with you, it's about her wanting to have some kind of control over her DD.

Don't use this as an opportunity to teach boundaries! What a terrible idea! This child is being treated badly enough without being served up to a shallow woman's anger.

The whole situation is awful for you and the child but you're making the best of it.

She obviously has issues. This is about her, nothing about you or her daughter.

You're worried about what some dickhead who has no interest in her own child thinks? Honestly you are probably doing amazing, use it as the chance to teach DSD that she can say no if she doesn't like what her "Mum" is saying to her.

Yes, you are BU to think it's a dig at you and to be upset by it. Even if it is a dig, I don't see how it makes any difference to you.
One of my much older and wiser friends once told me "a person I don't respect cannot offend me". I lived by it ever since.

It sounds like she is using this as a way of exerting some control.over her DD's life. She has very little input into her upbringing and it sounds like a way of staking a claim in her DD.

I don't think it's a dig at you but I can understand it will be annoying when you and your DH are doing the work of bringing your DSD up on a day to day basis.