They wouldn't have to spend story time on it. Luke and Leia probably investigated their family history prior to the events of the sequels.

Presuming Artoo has never had a memory flush, he's probably got a hologram of her in his memory somewhere.

Leia could have adopted Naboo as her home away from New Republic politics. (Or even live in Padme's apartment on Coruscant if it's still standing.) That and/or having Leia or Luke gaze solemnly at a portrait of Padme on the wall is enough.

Dear old Darth Dad is not something either Skywalker is going to want publicly known though. Especially if Leia has political enemies.