I'm a "take what you're offered and be grateful" kind of person, so I'd never do that!
I do remember being a new mum and having hoardes of visitors who only drank decaf coffee/herbal tea/non dairy milk/skimmed milk/weren't eating carbs/did I have a snack for their (insanely fussy) toddler/turned up with their dog (I have an angry cat)/ brought their mate (who I'd never met on day 4 of first baby).
People who turn up to visit a new mum and expect to be waited on are in a different category. Most people seem to realise you’ll be preoccupied with the baby and either bring food or help themselves?
I don’t understand why you didn’t just tell them to help themselves from the fridge/cupboard if you’d just had a baby?
Even if you weren’t holding baby it can be sore walking about and getting up and down, so why not say you’re sore/tired, please help yourselves?
I would have turned away the people with the dog; you don’t bring your dog into somebody’s home uninvited. Especially if they have a cat let alone a tiny baby.
Keeping tea, coffee, decaf and a few herbal tea sachets isn’t unusual. I’d just direct guests to the correct cupboard and fridge, say you can’t remember exactly what you have in but they’re welcome to help themselves. Maybe put some clean mugs and a biscuit box out if they’re the type to route through the entire kitchen?
If you don’t have non-dairy milk, just tell them. Most people don’t have it as a staple. I only buy it for dairy-intolerant guests I’m expecting well in advance, and only if they ask for it and specify the type eg soya/coconut/oat. My mum even carries little pots of lactose-free milk in her handbag! Plenty of types of tea (green, herbal etc) are designed to be used without milk. Visitors can take their tea/coffee black or have a glass of water/juice/cola or whatever you have in. I wouldn’t be making rounds of drinks if I’d just given birth, that would be DH’s job or the guests could make their own.
As for fussy toddlers, you could point the parent in the direction of the kitchen and invite them to prepare their child some fruit/cheese cubes/carrot sticks/crackers or whatever it is they eat. If you don’t have it in it’s not your problem, they can always take the toddler home.
I remember getting a take-away delivered for a group of hungry visitors who’d travelled a long way to see our first newborn. But I just gave them the stack of leaflets and they sorted out what they wanted with DH (while I held baby). It was Mediterranean type food they ordered so something for everyone even dairy free and gluten free. I can’t remember who paid but most of them offered to cover the whole bill, as did DH.