Give the kid another chance, and this time be sure the older girls get all one-on-one time. I know they had an hour free of little sister at the start of the play date, but frankly I always feel for older siblings who have to share play dates (even peripherally like in this case) with younger ones. The girl likely was very cross at being separated from your daughter; even though it was brief, she saw your child run home -- somewhere totally different from the park to her, even if the park seems like the back yard to you -- and she probably was mad at being what she thought of as excluded. It sounds like the girls had not seen each other for some time, and the visitor may have had high hopes for a play date with an old friend. That is not an excuse for her snippiness, of course, but it could be an explanation for it.
I agree that the girl was rude both to you and to your daughter but rather than "Playdate's over," you might have said, "That is not the way we talk and it's not allowed here." I find that pretty effective at shutting down backtalk even in kids my daughter's age (10) if it's delivered firmly but quietly -- and directly to the child's face. I found it even worked with a 12-year-old who was using some inappropriate language at summer camp. Said almost in a whisper but right next to the ear, it can stop them in their tracks because they know an adult has put them on notice!
I think that if your daughter's friend were consistently rude to your younger child, you could rethink things, but I would cut her (and your daughter, who wants to see her, right?) a break and not overthink this. Like I said -- I feel for kids who have to share play dates with siblings. I know siblings have to be included, to play nice, etc., but maybe next time arrange activities for the girls at home and something separate for your younger child so they just don't have to mingle.