Sounds like a sensible arrangement going forward OP. I am glad you have decided not to stop the little girl from coming to play despite the many suggestion that you do.
I am surprised tbh how many people have been nasty about vegans, won’t make ‘special’ or ‘fancy’ food or said they would not allow the child to play!
Vegan food can be cheap and easy. I think the falafels and fries was a good choice OP. Good on you for making the effort.
The mum sounds bonkers. Being vegan is fair enough though she should have told you at the outset. Saying no processed food is a bit much even if they avoid it at home.
As a rule, when people say no processed food, they usually still eat ‘lightly proceesed’ food such as bread, rice, pasta, tinned tomatoes etc. Just not the jars of sauce or ready meal level of processed.
For future ref the pasta and corn on the cob are a great start to a vegan meal. You just need another sauce. Tinned tomatoes, onion, garlic and mushrooms is my staple (though lots of kids don’t like mushrooms). You can get free from pesto or stir in sauces that are vegan. Chuck in peas/seeetcorn or any veg.
Otherwise beans on toast or jacket or potato waffles, add a bit of broccoli or salad on the side. Job done.
This may happen again so having a couple of ideas won’t hurt.