I can guess the genuine answer for this is “the prequels make no sense”, however I'm wondering if there's an in-universe answer.
At the end of Revenge of the Sith we see Luke get sent to his step uncle, and Leia adopted by the first person to put their hand up to have her. (A politician who no-one ran any background checks on, and no alarm bells were going off!)
I have a few problems with this. On the surface Leia got the best deal out of this, a life of luxury and space travel, whereas poor Luke got stuck in a desert, not allowed to join the academy and drinking blue milk.
Obviously it makes sense to split the two children, but did Padmé not have any family one of them could have gone with? She obviously had the family villa in Italy and seemed very well-respected and loved by her fellow Nabooians, hence the rather large funeral.
I can't believe her friends/family didn't know she was pregnant, or that with Coruscant’s fantastic medical care, questions weren't raised about whether children survived. (Cue a rather well-off angry old Naboo couple starting an investigation to find their missing grandchild, claiming it's a conspiracy).
So I suppose a TL/DR: did Padmé have any family? If yes, why didn’t one of the children go with them?