To not let DH go to this woman’s house?

A couple of things jump out at me… most people would not comment negatively on someone’s outfit if they’d only met a few times - this is overly familiar. Either she knows him better, or was trying to.
She is the sister of his friend’s wife… she has the potential to be around a lot if she wants to be.
if she really wanted to practice a haircut… hey bil, could you ask your mate if I can cut his hair? Or even said it in front of if the whole group. But contacting him on social media was unnecessary (and now of course has opened the channels of communication and likes).
So a discussion is in order, and DH has to really understand (rather than being excited that someone is chasing after him) that any contact with this woman (in person or on social media), and him wanting to persue this contact, has a very negative impact on your marriage, and to think carefully about what a decent husband would do. Because once trust is broken there is no coming back from.

Funnily enough I’ve had a similar situation with my very talented hairdresser… she suggested to my DH that he should train her at the gym (he is not a personal trainer, and was always quickly in and out of the gym due to us having two small children…). It made him uncomfortable and she was not invited back after that.

You are not being unreasonable.

I disagree. He promised to forsake all others, and a private haircut alone in a woman's house with just the two of them is not forsaking all others. They made a commitment, which means they are not free to do as they please in all circs.

Being a Cool Wife gets you nowhere.

If she could genuinely do with the practice, there's no earthly reason why she can't come to yours and do it, when you're both home.

But hairdressers usually have mannequin heads to practice on.

I cannot imagine inviting a married man to my house alone. The nerve! And it's a very thin pretext, since she has many other options than giving your husband a free haircut in the privacy of her own home. Going to yours/mannequin as I said, but also inviting him to a model night at the salon where she trains.

Actually, I've just realised, there's no point in cutting his hair at home alone. To learn, she should be doing it in the salon so that the instructor can correct and teach her as she cuts.

I smell a rat, OP. Not your husband - her.

I would honestly make a bit of a fuss. Men need some guidance, and some women need scaring off. A pointed "Don't you have hair mannequins to practise on?" and "Don't you need to be in the salon while you cut, so that the instructor can guide you?" Hell, I'd probably just message her myself and say "Kevin can't make it to your house, but if you have a model night at the salon with an instructor, he'd be happy to help." Then I'd tell him, "I've volunteered you for model nights at her salon!" Men are so obtuse about these things, he wouldn't realise that that means you've kicked her in her not-inconsiderable balls. I would take matters into my own hands. He can't do what he wants; he promised to forsake all others, and a private haircut alone with another woman at her house is not forsaking all others. If he wants to go around falling into honeytraps, he can be a single man.

Stake your claim, OP. I would.

Nah, he likes the thrill of the hairdresser trainee. He has a crush on her and it could develop further by the sound of it.

I'd say "oh, that's great that she's cutting your mop for free, you can have it done here and I'll get some nice biscuits in for her to have".

You will know by his answer what the story is.

Did he actually say he fancies her or did he say that she’s attractive? They are very different

It sounds like him wearing a naff jacket and getting a hair cut are the least of your problems.
let him go - hope he has an affair then you can get rid this woman will make it easier for you to LTB

You were right to say no

True, but she is likely doing extra cuts for the practice at her place as well as at friend's etc.

It's obv there is a mutual attraction, though. I mean, who just makes a personal comment about the attire of another person's partner like that, then the person changes and asks their approval. At the very least the guy could have said, Ok. My wife has already commented. I see I'm out numbered.
Or something. And made a joke.

Me too. But on MN it’s different apparently - men are controlling and women are totally reasonable 🙄

If he wants to cheat, he will find a way. You can’t keep him under lock and key and you can’t control him. Forbid him to go there if you like but it won’t make any difference - if he isn’t to be trusted, then he isn’t.

I'm a bit unhappy with the idea that you feel you have the power to 'allow' this or not.

They don’t usually go to the trainees house for a haircut. The college they train at have a salon. I used to go as whoever is tutoring them needs to inspect their work. I would be suspicious if he said he’s going to her house. Hairdressers usually go to clients house. Very few trained hairdressers cut hair in their home. I’ve had a few freelance cut mine and DC hair always in our home.

So if you know your husband - why on earth are you coming on here asking a bunch of random strangers if you are unreasonable? Presumably you think she fancies him and now you know he fancies her so you don’t want him to go - fine. Why is that unreasonable? If you know your husband - then you know the answer, we don’t hence some of the posts saying YABU.

An invested partner does not put themselves in potentially/compromising situations.
The DH is definitely acting suss and if he hasn't cheated is testing how far he can get.

OP should not have asked the questions she did (would you ask her out?, etc).

Be direct: I feel like your behaviour is showing interest in that woman and I'm not comfortable with it or you spending time with her. What do we need to talk about?

I would keep pushing to get the cards on the table. If the behaviour remains, increases, distance between us, whatever, I wouldn't just carry on hoping for the best, or nag for changes or discussions about it. I would just say, Not talking to me, flirtatious behaviour, rebuffing my concerns, spending time with her despite my concerns all point to cheating or considering it. If you don't want the marriage then it is time to separate.
And I would follow through.

Not in my world. In OP's place, I'd be using much more direct and vulgar language 😃

No! 😂

So what if they are confident?

Do people really talk like this?

Well fair enough!

I have to say, I find it bad manners to comment after someone has decided to wear something. (Bar obvious mistakes like it's a black tie dress code and they didn't realise.)

Any man telling me I looked stupid and to go get changed wouldn't know what had hit him... but I guess we are all different!

This! Maybe get your hair done too!

Jesus christ. At the stage you are bugging the situation just fucking break up

"Don't be wearing that hideous jacket when you go though, she hated it last time remember"

But humans DO make mistakes and surely sometimes you may need to point out to a partner they are being inconsiderate?

What flirting?