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SPOILER for the novel!
So in the novel, she realises it is the same potion when given it but is never told about Philip. Instead he gives her doctor an earlier iteration of it (with the full prescription so she doesn't have a problem giving it to Lucia), that he sneaks into a more effective headache medicine. So she takes it, and no-one is any the wiser.
She is not of Taran blood sadly, so a girl is born instead. But because it was an earlier version of the medicine, Philip tries to get involved by telling the Duke she'll die in childbirth if he doesn't. (She won't.) I forget the full details but that ploy is smashed. I think he dies in the end if I recall. Obviously there is no incest and continuing the bloodline though. (Though I think the girl CAN have kids with normal people? Not sure.)
The dream of her life was due to her having an ancient magic artifact. Basically in that timeline there was a thing of it being sold and her finding it again. But because it used up its magic power in THIS timeline (to give her the dream) it no longer exists. I forget how she got the artifact, but think it relates to her mother.
But the best bit is she can't really recall the later years of her life from the dream. But in fact, she meets the Duke during them. Damien has died, and the Duke left to wander cos he was all "fuck it, why bother anymore". That was why Philip was wandering and upset too - no continuing the bloodline. When she and the Duke meet they fall in love again. So basically they were destined to be together. Just it happened sooner in this timeline.
Anybody spoiler pls what's gonna happen nxt