Embarrassing family members are something you can import from real life to a game setting. But rather than harmless uncle Bernie and his awful jokes, make it auntie Maleficent di Cruella and her realm-spanning reign of sorcerous terror. Over and above being merely embarrassing, this can be downright dangerous when the peaceful villagers learn of your family relationship.
And it almost goes without saying in the context of Star Wars, but for even more fun, have the PCs unaware of the family connection until a suitable inopportune moment when they discover the awful truth.
R2-D2: —all I'm saying is a meatbag is still a meatbag even when it's a midi-chlorian cloud meatbag.
Luke: Anyway... This is pretty heavy. Vader's my dad, Princess is my sister, and I can't even think about what that means because I have to save her.
Luke: From him!
R2-D2: Yeah. This is a region of problems. We can't keep it private here. This ain't no Dagobah, it's Crowd City.
Luke: Dammit. This is gonna go public big time.
Luke: Rebellion led by the children of the tyrant... that's gonna go over great.
R2-D2: At first brush, it'll bleed discontent, but come on! Kids always rebel against their parents. It totally legitimises you.
Luke: I don't want to be legitimised by killing my own father!