I snapped earlier and I feel so awful now :(

It’s a restaurant (a fancy one at that) and not a playground.

children's meals are reduced in price because it is anticipated the costs will be offset by the adults who are also ordering. no wonder they were peeved at you!

Not this, she clearly states she didn’t order a meal for herself or pay the 90, she ordered the kids soup each, had some of their soup and ate the bread that was on the table. She states the price of kids meals and desserts, but only references buying the kids a bowl of soup each, which she ate some of, and then ate the bread on the table.

Loads of fine (and not so fine) dining restaurants only offer a set menu now as it saves ordering loads of different foods which may or may not be ordered. £90 for 3 courses is nowhere near Ritz prices (starters are £48, mains £75 and desert £30 on average - the tasting menu is £215 excluding wine). I also don't know any restaurants where an adult can share a child's meal.... You should have done your research as restaurants change all the time and what they did last year has no relevance to what they are doing now.

Why was colouring not allowed?
Did the staff want you to leave?

I've taken my kids to plenty of fancy restaurants and non have had a problem with drawing.
Its ipads without headphones that should be sent packing.

I suspect yes they did, as she was taking up a table, only ordered soup for the kids which she shared with them and ate the bread on the table them let the kids start colouring at the end.

I think I'd have probably left tbh when they said I could only have a £90 set menu, and promised the kids a takeaway at home instead.

If the staff were rude or stand offish then you were perfectly within your rights to not tip, but they probably thought you were being a bit strange by coming into a restaurant then not actually ordering any food. Or maybe they didn't want someone there who looked a bit green around the gills, they might've thought you were brewing a tummy bug.

Honestly, you're overthinking it.

A friend and I had snappy service at a restaurant for lunch yesterday. We'd sat down, and my friend asked to see the set menu, which was advertised outside, but wasn't on the table. The waitress bought it over, and we both decided to chose from there, as it seemed quite good value.
The waitress came back over to take the order, I said, "We're both going to order from the set menu." And she snapped back, "I know!"
We both looked at each other, thinking, "bit odd."
Ate our meal, didn't leave a tip, won't rush back. Honestly, it's not that serious.

Like other posters have said, as soon as you arrived and they told you it was a set menu, you should have left. If you snapped at the staff right at the start then it set the scene. Ordering food only for the children and eating the bread took the piss a bit. They had you labelled as a difficult customer.

All that said, it’s done now. Just don’t go back. You weren’t feeling well. Going out for a meal wasn’t the best idea. You know that now.

But you drove all the way to such a costly place as a particular treat, feeling unenthusiastic about food in general, and in the end just soup was ordered, and just for your children?
The ill-bred staff allowed you to sit there without ordering anything at all, and you reckoned soup alone, for children, would justify all that effort you made? Damn!

(I would anticipate an expensive restaurant refusing the adult diner’s request for a curtailed prix fixe meal I think, but I’m also surprised they allowed the table to order just bowls of soup, even if it was just for kids.
Presumably you ordered no wine, so this’d have been a very profitless cover.)

You poor thing! No doubt just staying seated awhile was making you feel better after your drive of course, but blimey if the only eager appetites were the girls’, McDonald’s might have thrilled them more!

[I think I must have skipped over essential info tbh, otherwise this disappointing (for OP) special treat sounds a bit wonky]

Good God, there’s some atrocious restaurant staff around by the sound of it, in places where a bit of natural decorum might be expected.