This 'twin paradox' is an odd result. The rationality of loving someone should be relatively stable in the face of changes outside of the relationship, such as facts about who else shares some of the properties of the beloved. (This is especially clear in cases of familial love, though I'm focusing here on romantic love.) We are led, it seems, to have to reject the view that the reasons for love are intrinsic properties of the beloved, on pains of admitting an unacceptable instability to our loving relationships.
One way to avoid this result is to refine our conception of how the properties of the beloved give rise to reasons to love. We might propose that Jill's beauty, for example, gives Jack a reason to love Jill, while Jane's beauty does not. How could this be? One explanation would be particularism or holism about reasons for love. On such a view, a property that Jill has may be a reason for Jack to love Jill, whereas if Jane has that property, it would not provide Jack with a reason to love Jane. There is something about the beauty being Jill's that matters for Jack's reasons; it's not beauty itself, which happens to be instantiated in Jill, that gives Jack a reason, but rather Jill's beauty.
If we're attracted to particularism about practical reasons in general, we might find this a plausible move. There's another tack we can take here, however.
We can grant that the intrinsic properties of someone provide reasons to enter a romantic relationship with someone, provided that one is not in a romantic relationship. But things might be more complicated when someone is already in a relationship. While Jack is in a relationship with Jill, for example, I'm supposing that Jill's beauty gives Jack reason to love Jill. What about Jane's beauty? Here's a proposal: In virtue of Jack's being in a relationship with Jill, Jane's intrinsic properties ought not give Jack any reason to love Jane (in a romantic way). This proposal is different from the particularist reply because we're not requiring a particularist construal of the reasons for love. Instead, we're considering that relationships put normative constraints on how we take things to be reasons. We can put it this way: being in an exclusive relationship means excluding the intrinsic properties of third parties from being reasons for love.
We saw that if we take a property view of reasons for love, the 'twin paradox' results. I proposed two solutions to this problem on behalf of the proponent of the property view, one giving a particularist account of the reasons, and one focusing on the normative demands of romantic relationships.
I'm just getting started in some of this literature, so what I'm saying here is very tentative. I don't yet know whether I want to endorse a property view, but I thought it worth pointing out some dialectical strategies for the property theorist that seem to have some merit.
 The example is based off a similar scenario in Niko Kolodny's "Love as Valuing a Relationship."