Family reunions can be... well, a lot of things. Exciting. Apprehensive. Fun. Awkward.
Just think of all the different and mixed feelings that people get at these occasions, and use those to inspire interesting roleplaying situations.
Commentary by memnarch (who has not seen the movie)
Ahahahahawhat? No seriously; all that build up with the visions around the lightsaber in the last movie and Luke just tosses it? Like, this makes some sense if the Director change had a completely different story in mind, but even so. This is a Star Wars movie, and one of the defining characteristics is Force Users with Lightsabers! I don't think Disney would let that not be a thing. So maybe this is the start of some weird training regimen? Yoda's original appearance is admittedly pretty bizarre in comparison to this so far, and it's not as if Luke would have a hard time Force Grabbing the lightsaber back.
As for the mother question, it seems more like Rey's parents are still Leia and Han(?), at least if the comic matches the movie well enough. While I suppose Parents/Adopted-Parents can be the shortening of Birth-Parents/Adopted-Parents, I've only personally seen Birth-Parents/Parents used. From my limited experiences then, I guess that could be due to a lack of interest to find out who one's Birth-Parents are, so that just leaves Parents as the only moniker usable. And from what it seems like, Luke disappeared a long time ago, though probably not when Rey was the same age he was compared to Anakin back in Episode III.
Anyway, I don't quite see how Luke thought that concealing Rey's actual lineage would help here. I mean, look where it got him! Fighting in a big war unprepared, grey hair, a chopped off limb, and living on a deserted island. Admittedly, the replacement robot hand looks pretty neat now, but it can't be easy maintaining that in a remote place surrounded by water. While I'm pretty sure Rey's got the skills to fight, I think it would have been better to try and prepare Rey for the Jedi/Sith stuff earlier. Probably not teenager age early, but at least something earlier than a "Surprise! Your grandpa killed off almost all of the Jedi! And you're adopted as well; I'm actually your Birth-Parent!"
GM: Let’s catch up with Rey and Luke on Ahch-To.
Rey: Finally! I’ve been standing here so long that the weather has turned sunny.
GM: Corey, you have the notes I gave you?
Luke: I take the sword Rey is offering.
Rey: So, like... you’re my father?
Luke: I’m so sorry, Rey. We had to conceal your parenthood to keep you safe.
Rey: But... I’m still a granddaughter of Anakin. How does that help?
Luke: First thing we have to do is get rid of this laser sword.
Luke: I toss it over my shoulder.
Rey: Wait. Tell me about my mother.
Luke: You just met your dad for the first time in a decade and you ask me about someone else?