Am I being unreasonable....

[Kitchenlight]

I arranged a dinner for friends visiting from abroad (their first time in three years). We agreed a small group - some people they know and some they'd like to get to know.
One of the invitees (A) is a good friend of my visitors (and someone I've known for a long time) and wrote to me ten days before the event and said her husband is away and her babysitter has cancelled. She asked if my children were free to babysit (they aren't) and said if they weren't could she bring her seven year old daughter along or she'd have to cancel. . Her daughter loves my visitors (and they her), and is a fabulous child who enjoys chatting to adults, but I really want an adult evening and her daughter will inevitably change the dynamic and shift my visitors attention away from the other adult guests.
I said I would prefer it to be an adults only evening but of course if she couldn't find a babysitter she should bring her daughter. A said she had no other options for babysitting so I offered to help her find someone and she said yes please. After asking around I eventually found a known, trusted and cheap babysitter and told A - who then said that actually she couldn't afford to pay for a babysitter as her financial situation is changing (they are a dual income professional family but her husband is about to go freelance). Also, she added, her daughter really wanted to come and might not get many other chances to see the visitors (A will be spending time with them on other days but she said it might be difficult to arrange much time for the visitors to see her daughter as she keeps weekends for family time).
I reiterated I'd prefer it to be an adult only evening and that I'd love her to be there and said I'd pay for the babysitter (it seemed the simplest solution). A said she couldn't accept me paying and reiterated her daughter really wanted to come and said they could both arrive early and leave early (which will be sad for my guests, but also awkward ... at what point will they leave? )
I'd like A to come and my friends would love to see her but I want an adult evening. It's taken effort to organise this (i asked everyone two months ago) and it's already quite stressful (unexpected events mean I'll get to my own dinner late). For context: I am a single parent on a single income so i am sympathetic to babysitting concerns and constraints.
AIBU - or should I just go with it?
And also, more importantly, can you think of any solutions that will make everyone happy?

That way they know the outline so shouldn’t throw you in it like you are afraid of.

come What may I am telling the truth in the same iron fist velvet glove I've been treated to. I'm too old to be pushed around

At this stage, I'd contact A to say "I have tried to remain impartial and I've even gone to the effort to arrange a baby sitter for you, you've said that your husband can look after your daughter and yet you insist on bringing her to the agreed 'Adults Only' evening that I've arranged. I have been informed by the other people who I've invited that they will be visiting you so there is absolutely no reason at all to bring your daughter to the evening. None. If you feel you cannot attend without your daughter, I'm sorry to say neither of you will be welcome. I really have tried to remedy this situation that you put me in but the situation cannot go on any longer. It's adults only. No children will be at the meal. Please respect the decision. I look forward to seeing you on X date and we can all catch up with you and your daughter at a later date"
Or something to that effect.

God, she sounds ghastly.

I have no objection to spending time with family or friends' kids in appropriate situations like BBQs or similar, but if I turned up to what I had expected to be an adult occasion like a dinner or cocktail party and the evening was dominated by some precious primary schooler, I'd be deeply unamused.

(And you just know this mother will be one of those 'show everybody your new ballet steps, Arabella!' types while all the adults sit around with rictus grins desperately wishing they were somewhere else.)

Yes, mention to the visitors that you do really want it to be adult only.

I agree with a few other posters. She didn't want a solution, she wanted to bring her daughter. The fact that she told her 7yo daughter about the event and then tried to guilt the OP by mentioning that the daughter refused to be babysat and was crying because she wanted to come tells me she had no intent of finding a sitter. She wanted to inject her child into an adults only event. You did the right thing by not caving into the pressure.

Don't lay a place for the daughter at the table. Make it tight enough that she won't fit. If she brings her, let her have her half hour in the spotlight but then let mum know she'll have to go in the other room and have a bag of crisps or something. Say to the daughter 'it's so lovely to have you here but we're doing grown ups only at the table so there's the tv next door'.
She'll absolutely ask the visitors if they mind the daughter joining the dinner - they won't be able to say no for fear of being rude to A and her daughter.

She is incredibly manipulative, no doubt her and her daughter will be very sad when your guests are at her house.

I would just be honest with them and say you was really looking forward to some adult only time with them for a good catch up

Jeez, This is utterly ridiculous the lengths she is going too.

I'd be rather blunt and direct now and ensure the other guests are aware of this drama, especially if she's inviting them to hers prior.

Tell her the guests have told you they are spending time with child and are in agreement the dinner is adult only for this occassion.

Is there not a group chat?

@Kitchenlight just out of curiosity what was your friendship like with this person before all this happened? And what do think it will look like going forward?
Keep strong and I hope your dinner party turns out the way you want it to.

@Kitchenlight, you've LITERALLY bent over backwards to accommodate A! A just wants to bring her child! That's all there is to it. While I understand that A doesn't want to go without her child, there comes a point when you have to be respectful of the host and NOT bring your kid if they are having an adults evening. Therefore, if I were you, I would tell her that you understand that she can't come this time, but would love to see her and her daughter at some other time! This isn't your fault. You LITERALLY found a sitter and told her you would pay! If she doesn't want to do that, that isn't on you! YOU are NBU! You did everything you could do to pay for a sitter and she still refused!

Visitors went to their house first. I asked if the mum was coming and they said no she has to babysit her daughter so she can't. She didnt tell them that her husband was coming back at nine and she cojkd have been her by 9.15. - which is when we eat.
everyone had a really really good time. I'm glad the daughter was not here as when my visitors went round to the house today they spent all the time with her and that is what they would have done if she was here. A child would have really altered the dynamic
the mum did not thank me for all the efforts I'd made re babysitting, nor did she drop me a note to say she couldn't make it when her husband came round after all

no one at dinner asked where she was - they don't seem to have noticed she wasnt there!

You got your dinner as planned with no derail and you also know a whole lot more about A op, so win win. A on the other hand has chopped her nose off to spite her face and that’s her problem. If you’re speaking to her just say oh yes we had a lovely night, shame you decided not to come!

Bloody rude of her to just not show up after saying she would come after her DH got back to look after the child but from everything else you have said about her it is not surprising. Glad you had an enjoyable evening.

The problem is that A was determined from the start to bring her child and never ever intended not to bring her. I didn't realise this. I took her at face value.

Exactly. Awful behaviour from A (and mini-A). Must have been a shock for you to see this all unfold. She has unmasked herself, really. Glad the evening went well.

no one at dinner asked where she was - they don't seem to have noticed she wasnt there!

But surely they weren't expecting her anyway.

They hd been to see her on the way & she had said that she wouldn't be there.

100% this.

Delighted you had the evening you were always intending to have. Shame that A decided to behave the way she did and as a result miss out.

Ah well.

The other guests I mean!

It's her party AND her, if ways to try and keep it strictly adult only for an evening then that is her right; if anything, her friend is acting extremely entitled in this situation. OP not only offered to help her find a babysitter that's both cheap AND decent, she also offered to pay when the friend said it was too expensive and when A said no to that, OP find someone who was willing to do it for free and STILL the friend said no and now it was because her kid really wanted to go (I wouldn't be surprised if she purposely hyped up her kid about it to try and guilt OP into saying yes). It was only when OP put her foot down and said "No" that A's husband is now able to watch her when he was supposedly gone/going to be gone around that time.
If you're willing to break your promise of an adult only evening just to make one person happy, then more power to you. I mean it's not OP's fault that A kept saying no to every babysitter she found her and A could've gone out and found one if she truly didn't like OP's choices.

TL;DR: OP tried helping A find a babysitter, friend kept saying no and giving excuses as to why.