AIBU to think DD should be able to spend her birthday how she wants

Just ignore any sulking , your daughter is an adult and making her own decisions, I’m amazed you’ve got to this age without this already cropping up .

You don’t need to call out MIL’s lie but you have to clarify the situation politely because otherwise it will cause negative attitude towards DD and it’s not fair. I would just put that it wasn’t like this at all as you had birthday takeaway and invited MIL for this but she declined to come. Just keep your answer simple, factual and polite.
DH is wrong by trying to sweep it under the carpet.

I'd have to put something in the chat, she's chosen to create drama by bringing other family members into it:

"I'm confused, we invited you to join us for dinner but you declined? Don't worry, DD understood and wasn't offended that you chose not to see her. As she is 20 years old, we don't 'allow' anyone to see her, she makes her own plans".

This is similar to my mother’s behaviour. Her mum did it to her and she always ran back to my grandmother to smooth things over. It has the opposite effect on me, I run a mile in the opposite direction and pay no attention until she snaps out of it.

Weird how some people behave.

Sulkers should be ignored. Adults who sulk are pathetic and shouldn’t be humoured. Your mil sounds manipulative and childish. Ignore her.

First of all I'd be straight out of that group chat, what a load of fuss over nothing. 2nd of all, your daughter is 20, you couldn't have made her stay home even if you wanted to. Lastly, MIL was given the opportunity to see your daughter. Your extended family seem stifling OP.

I don't want to alarm you, OP but I think we have the same MIL.

She's being ridiculous, of course. But your DH is completely wrong to tell you not to post on the group. Your MIL is the one who has deliberately chosen to cause drama by posting on the group chat and being economical with the truth, instead of messaging either of you privately.
You have every right to defend yourselves and your DD, and you don't need your DH's permission to do so. Since other people are now chipping in with their opinions on the matter despite not being aware of the full facts I think it's important to set the record straight.

I would respond with
"MIL, that's not true. We invited you over to see DD and have dinner with us, remember? You said no because you weren't happy that DD was going out after the meal. DD is an adult now with her own life, and we think it's lovely that she still wanted to have a birthday meal with her family today in between working, celebrating with friends and spending time with her boyfriend. It's a shame you decided not to join us".

Your MIL sounds awful

Glad to hear you've put your side across, at least people know now what happened.

So your husband would prefer his daughter is bad mouthed rather than stand up to his awful mother?
Nice🙄

@Stressedoutmummyof3 have you checked the replies since your post?

If he can't stand up to his mummy, he should at least he pleased that his daughter has inherited your spine.

Absolutely this!

Is she unable to grasp that DD is now an adult who makes her own decisions.

My dm has a thing about cards - birthday cards, anniversary cards, Christmas cards ... My 4dc are not that bothered and sometimes (often) the ones that live away - she doesn't seem to mind too much if ds sends a card or not (sexist) - don't send a card and I get grief. They're adults , it's not my problem! Anyway this year she was complaining about not getting an anniversary card from dd1 and the post came and she had sent a card. I think its a bit ridiculous. Certainly would give short shrift about having to see her on THEIR birthday. Your mil should have made the effort to fit in with dd's plans if it meant so much to her.

YANBU
Your MIL sounds controlling. Your DD is an adult and the days if her having to visit relatives without her choice are done. She can decide for herself who she wishes to spend her time with.

If your MIL can't treat your DD as an adult then leave her to sulk. She's being ridiculous.

I am a grandmother and I wouldn't dream of hijacking my grandchildren's birthdays! They are being very unreasonable and dare I say it seems really narcissistic. They need a good talking to.

This
She definitely needs calling out
No more tip toeing

Good on you. That needed to be said as Mrs Sulky will have conveniently forgot to mention that

Just put on the group chat that DD (add name) is an adult and makes her own choices in life and decides how she wants to spend her birthday! sorted!!

Sounds like my Mil
My poor Dd ( 21 ) gets messages all the time asking her when’s she’s going to visit bearing in mind Dd is at university just going into her third year about 90 minutes away she does come home at the weekend but works whilst she’s home and tries to spend time with her boyfriend or friends she then travels home straight from work on Sunday evening
Dd has asked mil to visit her at university as she finishes early on a Wednesday but mil always declines Dd had asked her to meet for coffee before she starts work on a Sunday but mil goes to church
Now Dd doesn’t even bother trying to see her as on the rare occasion she does ( half term usually which Dd always arranges ) all mil does is moan she never sees her and how Dd’s cousins who are also adults never have time for her because they have partners and work full time and have moved away ( how dare they have lives of their own )
It’s so ridiculous

She is 20! It's entirely up to her what she does with her life and her birthday, if she didn't want to spend it with her grandma (don't blame her, it'd be last on my list when I was 20) then that's her choice. If Gma is upset, then that is her perogative but she can't blame you, you're not your daughters keeper.
I'd personally say "sorry you feel that way but you were invited to dinner, we cannot control what dd does, she is 20 and has her own adult priorities and people who she wants to see, and we fully support her independent choices. It would be lovely to see you another time and we are really proud of how she still spends as much time as she can with her family despite juggling her job, her friends and her boyfriend"
I think it's purely a case of pointing out that she is an adult, with a full busy life who does what she wants and she has your full support to make those adult choices.

What a drama queen! Who has time for that nonsense. Let her sulk till the cows come home!

Mine have been spending their birthdays how they want to since they were about 14. Going out with friends for a meal not family.

Agreed. Please ignore her! Your daughter is a 20 year old woman, of course she wants to go out with her friends and boyfriend! Mil was offered a chance to come to tea! She refused!!! Make sure that’s on the group chat! When I was 18+ I was off out everywhere! My parents never said anything! It’s my day!