Not sure how to deal with this

I would talk quietly and calmly with the parents and ask them what they think the problem is ?
Something must have been said or done to make a 15 year old behave so rudely
It is the elephant in the room and you need some clues from your daughter or son I d certainly ask

Thank you all for your replies. I do appreciate it. I have known her for 7 years. She has always been quiet towards me - the back turning has developed over time. I am totally mystified by her behaviour and last week’s blatant back turning has really hurt me. They are a lovely family and the children are being taught so much that I respect - which makes it even more baffling. The adults must be aware so it kind of feels like an elephant in the room situation.
I think for now, I just need to see what transpires. Somehow to not saying hello to her doesn’t sit well with me but equally I don’t want to keep coming away from seeing them feeling hurt. Conundrum!

I doubt it is your fault, although I do wonder if somebody has said something in front of her about you or some event. I would ignore it for a while longer or if she does the same thing again immediately say, have I upset her in some way, whilst everyone is there and has seen what happened.

When was she adopted? How old was she? Has she behaved like this from the first time you saw her?

No wonder you’re upset. She’s certainly old enough to know just how rude and hurtful her behaviour is, and if she’s as bright and affectionate as you say there’s no excuse for it. Surely her parents have noticed too and know that you are upset by it? How could they not?

I certainly wouldn’t be walking up and being presented with the girl’s back. I’d do as Smileless suggests - if she looks at you, smile and speak to her, if she doesn’t, just let her be. She may surprise you, and herself, by acknowledging you. At least she won’t be given the chance to be so unkind.

Though no doubt someone will be along soon to tell you it’s somehow all your fault.

It depends on how you greet the whole family. If I turn up the children just carry on doing what they are and come in to say hello when they want, usually quickly, but I wouldn't make the effort to go up to her room for example, I'd wait till you saw her. Maybe what Smileless suggested.

It is very upsetting and puzzling,

I would want to ask the parents to see if there is anything I can do..it could be a damned you don't, and damned if you do situation, ie ignoring her would be held against you etc.

Sorry for your upset Temas. A few years back, one DGS began to behave much the way you described. After a few times of being ignored, we stopped attempting to interact with him-no hello, no conversation unless he initiated it. There were no problems with the other DGS.
Now he’s reverted back to being reasonably communicative; greetings, introductions to his girlfriend, information about his Uni course.
We didn’t ask about the ‘rudeness’ at the time and we certainly haven’t since.
I hope things improve for you.

I have the same problem I just smile say hello and leave it at that .
She’s old enough to know it’s rude

I would stop making a point of saying hello to her if she's turning her back on you Temas. That's extremely rude and someone should be telling her although at 15, she'll know what she's doing.

When you arrive, if she looks at you smile and say hello and if she doesn't, say nothing.

You could just ask her if you've inadvertently upset her..

My personal instinct, I think, would be to just ask (in a non-hostile way, of course). I'd ask the girl herself, then if I got nothing from her, I'd ask her parents if they knew of a reason why they think she is acting as she does.

I wouldn’t want to alienate the family either and I’d just carry on as before, but it is a very rude response. I’d ask the parents, tactfully, if they’re aware of any issue (she perceives) between her and you. It could just be a phase or something trivial. 🤞

That's quite distressing for you.

But what to do?

You can either accept that, for whatever reason, she has taken a dislike to you. It could even simply be the fact that you are not a blood relative - who knows with teenagers... and continue being friendly and polite, or ask the parents if they are aware of anything you might have done or said that has upset her.

I can't think that other members of the family are unaware of her behaviour. I know young people can be emotionally immature, and maybe not 'engage', but to deliberately turn her back on you when you enter a room is, frankly, rude. She can't be forced to be friendly if she doesn't feel 'friendly', but bad manners are bad manners.

If it were me, I'd want to clear the air - politely of course - but I'd be having a word with the parents, or whoever is responsible for her - not least to find out if there is anything at all that you have done, inadvertently, to upset her.

And, if I felt I couldn't do that - I'd extricate myself from any gatherings in which this child was included. If she were still a child, I'd ignore it and just continue to act friendly and polite - but she's on the cusp of womanhood and really should be behaving a tad more grown up. I wouldn't have tolerated my 15-year old acting like that towards anyone without good reason.

I know we have to tread carefully with young people but I do think sometimes we are too tolerant of bad manners.

Carry on as normal, it’s her problem not yours. Teenagers can be difficult to say the least.

Sadly it does sound as though she’s decided she dislikes you for whatever reason but I doubt there’s much you can do about it so maybe just try to accept it and not search for reasons. She might even come round if she thinks you’re no longer bothered by her attitude.
Other members of the family must know how she is with you so have they discussed it with you or even perhaps asked her to be more polite in your presence?
I certainly wouldn’t consider alienating yourself from the rest of the family over this problem with just one member.

If I were you, I would continue doing what you have been doing up to now.