and, yes, I'd like not to invite her really, but dd1 gets regular invites to her house and so I reciprocate. She and dd do get on very well and she's actually nice when food isn't on the agenda. (and even nicer when they're all playing upstairs away from me )

Good comments - thanks

I'd actually planned on making hotdogs and checked with her mum that she liked veggie sausages. But then I burned them (DER) and so went in to ask what she would like as alternative and offered pasta or spaghetti shapes on toast. She asked for pasta then I remembered dd1 saying they'd had salmon at her house so I asked if she'd like salmon with her pasta. She said yes... and the rest is history!

I wouldn't normally pander to anyone at our house. My dcs eat what's put in front of them and anything they don't like they leave, but they know there's no alternative. I do try to keep it simple when dd has friends back as most kids are fine with fish fingers and oven chips or pizza, etc. I certainly don't fuss around with a range of delicacies... I'm very about any fannying with food.

We had friends round the next night and our neighbour warned us that her dd (same age as dd1) was very fussy but I just put everything on the table and she very quietly just helped herself to plain jacket potatoes and very nicely asked if she could have some grated cheese for it. No complaints, no pulling of faces... that kind of 'fussy' I can do!

Why not serve the food in silence (or make a very obvious different conversation) and then leave the room whilst they start to eat - this way, the friend will have no-one to complain to, and she's probably less likely to complain to your DD - if she doesn't like it she just won't eat it.

Or you could make an agreement with her before hand - make it clear that there's 'this' for tea, and that's it, and she can go home if she doesn't want it.

Or be really sneaky and tell her that there's no other food in the house!

i always ask the mum what the child likes/will eat

i will then cook it but if they dont eat it, i dont worry

Oh, if you go for option 4 you are losing the chance to help the child change her behaviour and become socialised. She needs to see the difference between being a fussy little madam at home, and being invited to other people's houses. If she has no sn, she should make the connection and be able to decide whether she wants the treat enough to modify her behaviour.
If you either pander to her or drop her, a learning opportunity is lost and she'll continue being a pain in the bum.
My son can modify certain aspects of his behaviour for a short while if the motivation is high enough and he has time to be 'Aspie' afterwards in the privacy of his own home as a release.

Tell the mother that you are concerned her dd isn't having a good time, ask if there is anything that you need to know, such as spectrum or food issues.
Then either
1.child gets fed before she comes to you and can nibble
2. mother gives you a list of three or four things her daughter will eat without fuss
3.child manages without food or
4.you stop inviting her.
At the moment the child is setting the rules, and that needs to change and you need to stop trying to please her by offering delicacies prepared the way she wants them.
With my son, we go for option 2 where possible, or option 3

And stop worrying or feeling guilty about it. Then the level of irritation will drop.

I think I would be inclined not to have her for tea in future or just say well you only have this or that for tea and if it's not to her liking you will call her mum to take her home for her tea. If she realises the play date will be cut short she might well "back track" again.

One of DD1s friends used to be suprememly fussy. Told me once she would only eat meat if it was organic!

She went home for tea and wasn't invited again.

I tell them DS will be fine with toast and a piece of fruit.

DD1 (3.8) is quite fussy, and if she is tired is not likely to eat anything, even her favourites.
She went to a friends for lunch and I said to the other mother that if she didn't eat then not to keep offering her stuff, just whatever she was planning on making, and if she doesn't eat it, she will be hungry.
That's what we do at home, so that's what she did. She made tinned spaghetti hoops on toast, which I know DD1 won't eat (I thought she meant normal spaghetti, never mind) so DD1 had some toast.
I canm imagine how annoying it must be, I wouldn't pander to a guest who was being supremely awkward!

Oh and pizza.