DominicCobb said:

if these films are meant to be watched in chronological order, wouldn't it be weird to see Padme alive at the end of III and then never see or hear about her again until VI when we learn she died offscreen?

What if the last we see of Pademe, she's on Aalderan with Leia. Not acting as her mother, but a 'friend of the family' who can still keep an eye on her little girl. Then in IV when Alderaan is destroyed, the audience knows that Pademe was killed in the blast and that Vader just unknowingly killed his wife.