I think this can be simplified a little further. Rather than explicitly two bloodlines - Skywalkers and ‘Palpatines’ - I think it’s best if they’re essentially one and the same, simply two attempts at the whole ‘manipulate the midichlorians to create life’ thing (not that we’d use the M-word), both of which make powerful potential hosts, rich in the Force. Technically, by this interpretation, Anakin is a ‘Palpatine’ (in the loosest sense of the term), and Rey by the same token, but what we see in TRoS is Luke and Leia (and this plotline) essentially loosely reinterpreting ‘Skywalker’ to mean ‘a Palpatine creation who rose above it’.

This is well supported by the actual themes of the original TRoS, with Rey declaring herself Skywalker (with Luke and Leia’s approval). They’re saying “sure, be a Skywalker”, but here it’s loosely implicitly “like us you’re Palpatine offspring in the light, so the Skywalker name suits you too”.

I’m not saying we should make any of that explicit in the text, but that we should maybe do away with the “bloodline” angle and simply refer to Vader (and his heirs) and Rey, as all simply products of Palpatine’s will - with Vader as his first attempt and Rey as his (perfected if you like) second. So technically Luke and Leia are ‘Palpatines’ too by this interpretation, albeit in a way we wouldn’t make explicit.