Just for the sake of completeness: "legal" is a German word as well that fits into this context.
You might want to add this. Rechtlich and gesetzlich are somewhat similar terms. The difference between the two boils down to the difference between Recht und Gesetz.
Recht is considered the entirety of all valid laws at any given time, so rechlicht is stemming from the entirety of laws. Both rechtlich and gesetzlich can be used for both your English meanings 1. The distinction is, once again, that gesetzlich often refers to obligations or supports stemming from single laws or small subsets thereof while rechtlich is often taken to mean the overarching entirety.
Sie dazu sind rechtlich verpflichtet legal obligation. Something single taken unicorn meaning is probably written in more than one place. Aus rechtlicher Sicht legal point of view; closer to meaning 1 spricht nichts gegen Ihre Ansprüche.
Therefore, a gesetzlicher Vertreter is a representative as specified by a single or a small subset of laws. Typically, your parents if you are a minor.
A rechtlicher Vertreter, like the Rechtsvertreter is somebody who represents you in the face of the entirety of laws — a lawyer. This interpretation is typically not intended with rechtlich.