Ds has just completed a a PIR (Politics and International Relations) degree at Aberdeen Uni ( and managed to get a job in the field he wanted, Public Affairs
). He only went to the Open Day there under duress (in fact, it was the only one I went round with him) but he loved it when he visited. He hated St Andrews, as he felt it was too claustrophobic (which I said was fine: some people love it - as I did when I went there - a loooong time ago 
- but it can indeed be intense/claustrophobic).
He applied to Edinburgh (2 different courses), Strathclyde (but not Glasgow as he felt it wasn't as strong on his interests in IR as Strathclyde), Dundee and Aberdeen. He'd got, iirc (
) 3 x A (Maths, Geography and Physics) and 2 x B (English and Chemistry) for his Highers and was doing 2 Advanced Highers (Maths and Physics) and a crash Higher in Modern Studies. The latter was fortuitous as he changed his mind about what what he wanted to do at Uni between S5 and S6, from Maths/Physics/Astrophysics to International Relations 
He ended up with two unconditionals: one from Strathclyde and the other from Aberdeen and rejections from the other two. But he was happy as he'd already decided he liked Aberdeen (and he got the Unconditional offer from Strathclyde very quickly which meant he could relax
)
He was able to study a wide range of subjects in 1st and 2nd year alongside his Politics and International Relations modules, including history, philosophy, economics and sociology. He particularly enjoyed macro-sociology which he considered taking as part of a joint honours - but he was too interested in the range of PIR options (and his interest had shifted from IR to Politics).
Your dd shouldn't think she's not "good" enough
. As others have said, there are 5 choices on the UCAS form, so she could include aspirational choices as a few of them. She should go to a few open days and find out what's on offer. Hopefully, she'll see that she can go to a good Uni and that they're not just for private school kids.
Have a think about Aberdeen - the ds of a friend I met on MN ended up applying as an aspirational choice after I told her about ds' experience and how much he was enjoying Aberdeen. Her ds got a conditional offer and he is just going into his 4th year/Senior Honours year (he's a year younger than ds).
Ds went to a Glasgow state school that has a very high proportion of SIMD1 and 2 - but it also has a very mixed demographic (so we ourselves live in a leafy bit of Pollokshields, technically not in its catchment). No tutoring and the school, although very supportive of and aspirational for its young people, does not spoon feed them and encourages them to be resilient. It was something that ds emphasised in his personal statement and he's convinced that that helped him get his offers. (He also described well why he'd developed his interest in IR, because of Mandela I have a South African heritage ).