I'll try to keep it brief, but my patience is wearing thin!
We've lived in this house since Dd was two. The little girl next door is the same age. So obviously they are very close. They've always had similar interests and never ever fallen out. They're both very laid back, Which helps.
Since they've been at senior school they've both developed new friendships, some are with the same people, some not. They still spend a lot of their time outside school together though.
Anyway, one girl has taken a complete dislike to my Dd but a real shine to friend. Fine. I have always told Dd that not everyone will like you and you won't like everyone, just be respectful and polite and get on with your day. Unfortunately this girl is just plain nasty, and the Mum seems completely blind to it.
Incidents include - reducing Dd to tears on her birthday by ignoring, and encouraging 3 other girls to ignore her while they were at school and on the way home. Because, in her words, she didn't like that dd and her friends were talking about what they would do at her sleepover. Incidentally she was invited but doesn't 'do' sleepovers.
I did call the Mum on this occasion because it was extreme in my opinion, and the girl was made to apologise.
Calling friend to invite out, friend says can't because Loulou-Dd is here. To which she said 'can't she go home, she only lives next door?!'. Her mum was heard shouting in the background while girl sulked 'is that Loulou-Dd again, thinking the world revolves around her?' This example has actually happened more than once.
There are other examples, but I won't go on more ! Basically one of the big issues, and the reason my Dd is out of favour is because she has rules and boundaries. She has a set amount of pocket money, which she has to budget all her monthly activities with. Once it's gone it's gone. The girl is fond of shopping trips for no reason. These trips cost about £15 once travel and lunch are factored in, which IMO is a waste of money if you have no need to shop. She also likes to do activities like ice skating or swimming, but at 7 pm! So they only get an hour before they close, whereas I try to encourage Dd to do them at the weekend or during the day as better value for money. The girl doesn't have sensible curfews IMO! 
she's allowed out until 9 (they're 12) then travels home alone... Maybe 3/4 mile. Dd does have a curfew, I don't let her have my debit card to go shopping, she does chores, and has to spend time revising and doing homework. All very boring! Unfortunately mum next door tries to enforce rules, but the Dc's just play her up until she gives in. Also mums new partner is quite well off and seems to be trying to buy them, so no money issues.
So, fast forward to today. Mum next door asks if her Dd can stay with us so she can go away for her b'day. No problem. She'll bring her Dd over when they've finished an activity this Am, probably about 11. Next door Mum knocks at 11 to say her Dd is with the girl still at activity, girls Mum will drop off at lunchtime. Ok. We were still having baths and tidying, so no problem. But AIBU to think that actually she should have been made to come back?
It's now 3, and she still isn't here. Dd didn't make any plans because she was expecting her friend. What a waste of a day for her. AIBU to think its poor form for the girls mum to be seemingly encouraging it, and not sticking to the lunchtime drop off?
I really try not to interfere because I do think it's better for them to find their own way, but bloody grrrrrr!! Unfortunately because we live next door it's hard to get away from the friend, and in turn the girl. So how do I handle things today and going forward?
Sorry this has been epic but I wanted to put it in context and not drip feed.