Social Etiquette of Parenting

I had a strange, fantastical idea early on that as I adjusted to parenting that it would become easier as time went on.
(I'll wait a moment whilst any other parents who might read this, pick themselves up from rolling around on the floor laughing).

I was, of course, wrong. It's not exactly that it gets harder and harder, it's more that everytime you find a solution to a difficulty, another one (or two, or ten) quandries appear to replace it!
We live on a relatively quiet cul-de-sac. There is a small group of approx 4 children who regularly play out on the street without visible parental supervision (although I am sure that they are being kept an eye on, but mum/dad isn't sat in the front garden). They are all at least 2 or 3 years older than Ellie, and live near each other at the other end of the street. It's a nice street - everyone says hi to each other, and smiles on passing, but you don't really have conversations with people other than your next door neighbour. (unless there is some big 'crisis' occuring). Ellie's friend Evie also lives on a cul-de-sac, but the grown ups there appear to be more sociable, and I get the impression that they chat together, or take turns to be 'supervising adult' whilst the children play.
I'd quite like Ellie to be able to play out on the street with the others, but a) I think she's a little young to be out on the road yet and b) we've not made friends with the other children yet. So, I put this problem to one side until she is older.
However, recently a 9 yr old, who I do not recognise from the street has been coming round to see our cat (ie we keep finding her sat/standing in our front garden stroking or holding our cat). This has developed quite rapidly into her coming into our back garden when we are there (I hope not, when we are not) and even into our house - chasing after our poor cat, encouraged by Ellie. I had hoped that she might play with Ellie, but if we point out that the cat is now hiding and looking very stressed and perhaps should be left alone, then she gets on her bike (literally) and heads off. Conscious that our back garden is very private, I make a point of asking if her parents know where she is when she comes into our garden. To which, she says 'yes' - although I doubt the accuracy of this.
Short of insisting that she takes me back to her house to meet her parents, I am unsure what do about her prescence in our garden, and what her parents might make of her being hidden out of sight in our back garden. And, I'm not even sure I want her round at all, if she is going to upset Ellie by dashing off as soon as the cat is unavailable without even saying goodbye, when Ellie was really enjoying spending time with the 'big girl'.

Hmmm.