There's nothing "weird" about the other mum's behaviour, as you've suggested @Idliketobeamillionaire . It's annoying to have a visiting child asking for treats when you've already given them snacks. I'm sure the mum has valid reasons for saying no further snacks. It's not like she hasn't fed her at all.
I think the mum might feel annoyed if you send food over to her house. It's not fair on her boy, is it, to watch your dd eating in front of him and he's not allowed? If your dd really can't go very long without food then she should pop back to your house for a healthy snack since she's only 2 doors away. She can then return to her friend's house, if allowed by the other mum, to continue playing. Your dd shouldn't be asking for food at other people's houses and I suspect she's only asking in order to get junk food.
Why are you ignoring so many helpful posts? Posters have recognised there might be another issue here, causing your dd's hunger, but you're not responding. The medication might not be the only reason that she's so hungry.
Not drinking enough fluids can cause feelings of hunger as can eating a diet that's mainly carbs. Based on what you've written, she is eating a lot of white carbs, fruit and treats. She had pasta for lunch, followed by a sandwich. Then toast and strawberries. White bread and pasta? What was served with the pasta, what sandwich fillings? Fruit is healthy but can be high in sugar, depending on type. You haven't mentioned protein or healthy fats at all.
She needs lots of protein and some fat to feel full, otherwise her blood sugar levels will be erratic and she'll feel hungry all the time. She needs to eat protein/fat at the same time she's having fruit, rice cakes, simple carbs, etc, to stop her blood sugar levels spiking, then crashing, leading to hunger.
Unbalanced blood sugar levels can also lead to poor concentration levels and mood swings. How is she managing at school, with such hunger issues? Perhaps change your food choices for her, give her a combination of protein, some fat plus ( ideally complex) carbs at every meal and you might find that she isn't so hungry and can go for longer periods of time without eating. Plus give her lots of (sugar free) fluids.