Just to be clear: the dragon-blooded elf queen ruled in her own right (without remarriage) after her husband died? This is an unusual situation in most cases, because titles are usually not inherited by one's spouse, even historically. E.g. England has only had two "coregencies," where the King and Queen ruled jointly. In both cases, the spouse with the legitimate claim to the throne of England died before the other spouse (Mary I and Mary II, as it happens), and the crown of England passed to the next closest claimant, not the spouse.

So you'll want to consider what rules might be involved for the Elf queen having a claim--since this is very different from most real-world monarchies, that could be very significant.

Formally speaking, there are two key issues here. First, it sounds like the "default" legal succession goes to the claimant's eldest child regardless of gender. This is called "absolute cognatic primogeniture": closeness of descent is the only relevant metric, not the gender of the person by which the inheritance is obtained ("absolute cognatic.") Further, children of each preferred inheritor are given primacy, so if the monarch has three children, and two grandchildren by their eldest child (and no other grandchildren), then the inheritance would go Child 1, Grandchild A, Grandchild B, Child 2, Child 3. (This is how the current English succession works, hence why Prince Harry is now 5th in line for the throne, after his brother and his brother's three children.)

Second, however, it sounds like legally the reigning monarch may choose whomever they wish to be their successor. (This may be how the elf queen came to power; if she was chosen to be her husband's successor, then she would rule in her own right despite not being part of the royal line properly.)

This creates a dynastic split, because these two rules do not agree: according to the former "default" rule, the eldest child of the eldest child of...(etc.) is the (one and only) valid claimant of the crown once the old queen dies. According to the latter rule, however, the queen (if she is in fact ruling directly) could select anyone she wishes, but it sounds like her death was sudden.

This leads to at least four likely events:

There will be a significant number of "pretenders" among the king's human descendants. Note, this word is not the usual meaning of "pretender," that is, it does not imply that the claim is faked or imaginary. It simply means someone who is claiming to deserve the title, whether or not they actually do. (The fact that most pretenders will end up being false ones is where the modern sense of "pretend" came from.) It's been, as you say, 500 years and the king may have had living great-grandchildren when he died. Even if we assume 25 year generations (which is a long time for a medieval society), you're talking at least 20 generations separating things. Considering how difficult it is for us to get documentary records of things that occurred 500 years ago, it's going to be difficult to prove conclusively what the "eldest child of eldest child" line is--and you can bet your bottom dollar there will be folks claiming to be descended from illegitimate children somewhere in that mass. Thus, there will almost certainly be several forces trying to find the true valid claimant, set up an easily-controlled and legitimate-seeming fake, or just profit off of sponsoring someone with a useful but incomplete claim.

There's almost guaranteed to be at least one faked will from the Queen saying who she chose to succeed her. Probably multiple. It's possible there's a real will, but it's also just as possible that there never was a real will, that she had indefinitely put off making such a difficult decision until she "knew it needed to happen." This leads to all sorts of skullduggery and ways one might try to verify or cast doubt upon a claimed will, and (as noted in other places) efforts to affect the mechanisms of state involved in actually recognizing and accepting the authenticity or falsity of a given document.

There will be at least one ploy to corrupt the mechanisms by which the choice is made. The whole point of monarchy is to build up legitimacy, so that the government can rule via social pressure, rather than ruling via force of arms. Because ruling via force of arms is incredibly unstable and invites far too much trouble. But legitimacy is a weird wibbly-wobbly timey-wimey consensus-and-observation kind of thing, arising from the mix of institutions and social mores and performance of a role etc. etc. (none of which means it is illegitimate or insincere per se; just that "cause" and "effect" are muddy and determined by human choices, not by physical constraints.) So there has to be some kind of aristocracy or bureaucracy that will need to "approve" of whomever makes the claim--and that invites a whole host of other questions. You'll want to consider what the legislature is like (few monarchs rule so directly that they write all laws personally!), what the tax-collection scheme is like, whether there are powerful aristocrats who don't want to rule but do want to control, etc. etc.

Civil war. The Wars of the Roses happened for reasons very similar to the above. Essentially, there were two claims to the throne, where one was clearly senior (coming from an elder son) but had been inherited through a female intermediary, while the other was clearly junior (coming from a younger son) but originally exclusively through male-line inheritance. This conflict between seniority and male-preference emboldened the two houses, Lancaster and York, but eventually through both external violence and internal strife resulted in the extinction of the male line on both sides, until Henry Tudor (inheriting a claim through his mother) married his second cousin once removed, Elizabeth of York, thus uniting the houses of York and Lancaster into the new House of Tudor. So, if you like, you could have a similar sort of thing come up, with a (possibly loveless) relationship proposed between highly eligible claimants on both sides, allowing for the possibility of a "reuniting" of the two houses.

You probably also want to give an actual name to the two houses involved here, simply because it will make it a lot easier to talk about. Always having to say "the human descendants"/"the part-elf descendants" will get awkward fast.

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