Has anyone ever sued Tui?

As others have advised, start with ABTA. Depending on how you paid could you also raise a chargeback claim under the reasoning of not received, or not as described?

In my experience TUI are a dreadful company to deal with. I have booked a holiday through both First Choice and TUI and both times had a lengthy drawn out process to receive compensation/refunds. They most definitely try to make the process as difficult as possible, and the rep in resort did everything possible to avoid taking action. I also found them sneaky/underhand, eg. they sent a bottle of wine and some fruit up to our room as an apology for a specific incident and then when I was following up on the wider complaint back home they claimed I had accepted this as compensation for the issues! I would never book with them again.

Stick with it OP, they'll pay out in the end.

And they have offered her less than that
Yes, but what they exactly offered?

I had a similar issue with BA. I was helped by Which? The Consumer Site and they advised that BA was part of an arbitration scheme. It might be worth checking if TUI is as well? This involved me filling in some forms and if I lost the maximum cost was £50. It took a couple of months but of course I won and BA paid up.

This happend to us. Tui rep couldn't/wouldn't sort and as an excuse as to why not was racist about the attitudes of the people in the country we were in. I kicked off repeatedly with the hotel and got moved to a slightly better set of rooms after a cleaner told me they were empty but they were not the ones I'd paid for. Tui routinely ignore all complaints and force you to go to Abta. They will not respond to anything you send them. I did the Abta thing, got offered £400 off another holiday (upgrade cost £750) I could have gone to the next stage which would have cost £120 but I had run out of steam at that point so I just vowed never to use them again.

@KatStratford

I would want more than just a refund of money for the services you didn't receive.

You should receive compensation for having a different holiday than you booked and also for all the hassle on holiday.

OP says in the first post...

So for example she paid £3000 for a premium holiday with extras. She gets there to find that she isn't getting that, she's getting the basic holiday without the extras which was £2000. So she complained and asked Tui to at the very least refund the cost difference between the basic and the premium. And they have offered her less than that.

I'm confused as to wha is the difference between what they are offering and what you've asked for.

To me this is straight forward - you paid for what you don't get - yes send them a letter before action - no action, small claims for the difference plus cost if small claims plus say £500 for 'hassle'

If I were you I would make them an offer - work out what you are owed, and put it to them in a letter and say that if they don't settle you will be pursuing a formal avenue of redress.

It took me 3 years to settle with Tui and ended up at County Court with a (lovely, sympathetic) judge and an excellent barrister.

I would feel both anxious and annoyed, just like OP said she felt. Anxious waiting for my complaint to be sorted, anxious and annoyed because it hasn’t been

You would feel annoyed. This is not the same as feeling anxious. You might get wound up but again that's not the same as feeling anxious.
People are not giving arsey replies. Just because it's something you don't agree with that doesn't make it arsey.
OP you have very valid reason for complaint. We paid for X and we got Y. This spoilt our enjoyment as we had difficulty sorting it out due to reasons ABC.
Keep it factual

Not Tui - but this time last year had an ongoing dispute about a pension transfer from one provider to another which dragged on for around 7 months.

The ONLY thing which worked was when I went to Sally Hamilton at This is Money - there are other consumer "champions" with other media. Sorted within days, and a good dollop of compensation too. Would advise that before going legal.

Send them a Letter of Claim (aka Letter Before Action). If they still won’t settle take them to the Small Claims Court. The chances of them settling are extremely high.

Try not to attach emotion to it, it's actually really good that they are admitting fault. Just get all the facts and evidence down. I think, remembering it I complained to both ABTA and TUI (they have an online complaint system).

Long and short of it, you didn't get the product that you paid for, which anyone would feel stressed about. ABTA is the way to go. As another poster said they have a simple portal where you can upload info for the complaint.
You may not hear anything for a while, however i would 99% say that you will get compensation with evidence.

Feeling stressed and anxious about a situation is NOT having anxiety
Having said that you ddin't get what you paid for OP and I am sure it affected your holiday so try SM first and also complain to ABTA. If all else fails small claims court

They are honestly the worst company ever and I'll never book with them again.

This should be a pretty straightforward breach of contract claim. Go via ABTA in the first instance. There is a portal where you will be able to upload a description of your claim and supporting evidence.

I’m not sure why you’re getting arsey replies about stress and anxiety. I too would feel stressed and anxious if I had paid for something, not got what I had paid for, and then the company didn’t resolve it for me, especially something like a holiday, which needs to be resolved immediately, or at least refunded

You want the difference between what you paid and what you got, as well as something for loss of enjoyment (Google Jarvis v Swan Tours)

Not Tui, but took Thomson (who they took over) to court twice and won twice. Both times they played hard ball with derisory compensation offers, so I issued small claims court papers and they took it right up to the day before the court hearing both times, before I received (the day before) a special delivery letter with their cheque for the full amount I was claiming for! Both times it was for the full cost of the holiday plus extra expenses incurred (all receipted) due to their incompetence and not providing all aspects of the holiday booked which caused us to spend a lot of time during the holiday complaining to their reps and/ the hotel management. Their complaints dept are just a typical "fob you off" department (just like the NHS) hoping to wear you down so you give up.

Anxiety?
Pissed off fair enough but anxiety?