I have read the full thread, unlike some of the commentators on here based on the comments/questions!
You were not unreasonable at all. You chose somewhere they advertised itself as family friendly and that groups are welcome. They don't take bookings, so you couldn't forewarn them that you were coming.
They were happy to seat you, including the owner himself setting the tables up for you.
That woman was ridiculously rude. The people on here saying you shouldn't have said anything are very clearly the sort that are like that woman - loud and obnoxious making it clear they don't like something but act all hurt, fragile and shocked of someone dares to call them out on it. I bet that's why the poster further up felt the need to repost it, as it was a completely unnecessary repetition.
Now that you have added the bit about the headscarves the comment comes across as a racist one completely. If that had been a white family without headscarves that miserable bitch wouldn't have said anything at all. Guaranteed.
You were right to walk out - I'm glad you were welcomed at the other cafe.
The posters presuming that ALL children are a nightmare in public think that so find that. They're looking for the bad behaviour so will find it. E.g. A family could sit there good as gold, but the kids whinge for a few minutes at the end because they're bored - THAT will be what they remember. Not the hour of sitting nicely!
My kids rarely get to go out because we can't afford it and they can't behave well enough. We told them they don't get another chance until they show us how well they can behave when eating a meal at home. The last time we went out they were much better. I do think that sometimes people are trying to teach them how to behave and perhaps a bit of bad behaviour will result in better behaviour if that makes sense. Sometimes they might not even know that they'll behave like that because they haven't taken them out before or they've behaved in the past.
Ignore the judgey people on here. I love all children and thorough enjoy being in their company and will always talk to children that talk to me! I always have a houseful of kids when I'm at home (annual leave or weekends as I work full time) as my kids know I love having their friends round because they all get on so well. My 'd'H is a miserable git who clearly hates children though......