Well, first my disclaimer - I'm not a behaviourist or a trainer, and there are lots of very knowedgeable and helpful people on here.
My interpretation would be that during her critical socialisation period she was with the first owners, and the existing dog did not react well to her. It's very unusual for a pup not to get on with another dog - they will back down and just want to be accepted by older dogs when they are tiny. So I think it was more a case of the existing dog not getting on with the pup, rather than vice versa, iyswim. That could have taken the form of normal older dog putting pup in its place behaviour, which inexperienced owners may not have been able to understand, or the existing dog itself may have been poorly socialised with other dogs and so may really have been aggressive to the pup.
In any case, that would account for why she is nervous around other dogs, or she may just have a timid and nervous disposition. That would also account for why she is 'clingy'.
tbh, if it were me, I would get a behaviourist to assess her, because of course it's very hard for anyone to say what her character is without having seen her.
In the meantime, you can try to socialise her as much as possible with well behaved dogs. Do not push her out of her comfort zone - allow her to go as slowly as she needs to, but also do not try to soothe or reassure her when she shows fear. That can be interpreted by the dog as a reward for that behaviour, and they will do it even more just to 'please' you. Try to be relaxed and confident round her (I'm sure you are!) and that wil rub off on her.
A training class would be good - it would give her something to occupy her mind and also introduce her to other dogs in a controlled environment.
Right, will stop wittering on now and give some of the other very smart and helpful people on here give their advice too.
Do keep us posted, please