OK, but I find that I can only answer the rightness of Rights questions within the context of morality (as Locke himself did), so I should just answer for myself then.
Here’s how I see it. I don’t agree that property ownership or any other Right is justified by Natural Law, and therefore somehow inherently real/genuine and inalienable, or can only be contravened by invoking some other aspect of Natural Law (like equality). I reject Locke’s framing, for reasons I’ve given.
To answer the question for myself I apply my own framing, which grounds the justification for Rights within a moral framework which overall tends towards trying to promote well-being. And I see that as the appropriate role for Government in a social contract with its citizens. In that framing, laws and rights are contingent on this underlying aim.
So I view Rights as a constructed tool for ensuring citizens have the basic necessities to afford the opportunity to flourish. And a baseline protection against Might is Right, including the tyranny of the majority which might form a consensus against minorities.
In your scenario invoking the Right to Own Property, while in many circs useful, acts against the wellbeing of the newcomers in a way which deprives them of the overall goal of being able to flourish. So the Right being asserted here wouldn’t be doing the job it’s supposed to, and ought not hold.
While Locke invokes Fairness or Equality, as justifying consideration of the competing interests at stake, I’d say these are also aspects of wellbeing, which is the ultimate test for me. And the state of having interests in what happens to you (your well-being) is as close as we can get to self-justifying Oughts, and subsequent Rights. There’s no need to rely on God or Nature imbuing us with Rights, it’s simply that what happens to us matters to us, we have a genuine stake in outcomes.
TLDR -
The existing farmer family will have some fewer resources if they share, but the new family will suffer harshly if not. And that’s wrong.