I’m not sure it’s quite rivalry but I do think it all stems from the fostering. From her parents descriptions in various articles singing their praises it sounds like it was a particularly chaotic house as they (or certainly big D at least) prided themselves on taking “challenging” children - there are descriptions of being on their third front door and a sink pulled off the wall amongst other things.
From everything Jack has said and given away about herself, this sounds like an environment that genuinely would have been absolute hell for her and it is hard for the bio children in that situation to speak out sometimes because all they tend to get is “But you’re so lucky compared to X, don’t you know what Y has been through, you should have compassion!” which I believe she got and is the cause of the resentment that absolutely shines through whenever she talks about fostering.
Her parents fostering is obviously admirable… but everything they and Jack have said makes me believe it was awful for Jack. None of this justifies what she does now obviously, but I reckon it’s where it’s all rooted.
ETA: and I also believe that apart from the behaviour she did struggle with attachment, even if her description of sharing a bedroom isn’t accurate - look how fast she goes from 0-Marriage with everyone who she shags, clear attachment issues there, I can see her getting attached to certain foster children and then being genuinely heartbroken over and over when they were then moved.