As to whether Padmé had a family, the answer is a firm yes.
Her parents and family are mentioned in both the Attack of the Clones novelisation and the original film script.
“No, but I-” the distracted Anakin started to answer, but he was
interrupted by the squeals of two little girls, running out from the
yard toward his companion.
“Aunt Padmé! Aunt Padmé!”
Padmé’s smile went as wide as Anakin had ever seen it and she rushed
ahead, bending low to scoop the pair, who looked to be no more than a
few years old, one a bit taller than the other, into her arms. One had
hair short and blond and curly, the other, the older of the two, had
hair that resembled Padmé's.
“Ryoo! Pooja!” Padmé cried, hugging them and twirling them about. “I’m
so happy to see you!” She kissed them both and set them down, then
took them by the hand and led them toward Anakin.
Not exactly like Padmé, Anakin noted. She was a little older, a little
heavier, and a little more… worn, was the only word he could think of.
But not in a bad way. Yes, he could see it now, he thought, watching
as she and Padmé hugged tightly. This was whom Padmé could become-more
settled, more content, perhaps. Considering the amazing resemblance,
Anakin was hardly surprised when Padmé introduced the woman as her
“Mom and Dad will be so happy to see you,” Sola said to Padmé. “It’s
been a difficult few weeks.”
The next introductions were a bit more uncomfortable, but only for a
moment, as Padmé showed Anakin to Ruwee, her father, a
strong-shouldered man with a face that was plain and strong and
compassionate all at once. He wore his brown hair short, but still it
was a bit out of place, a bit… comfortable. Padmé introduced Jobal
next, and Anakin knew that the woman was her mother without being
told. The moment he met her, he understood where Padmé had gotten her
innocent and sincere smile, a look that could disarm a mob of
bloodthirsty Gamorrean raiders. Jobal’s face had that same comforting
quality, that same obvious generosity.
There were even scenes filmed (that were ultimately deleted) in which we meet her extended family and learn more about Padmé's
(timestamps 09:01 and 05:01 are especially illuminating)
When it comes to the question of why her family didn't come looking for her children, the simplest answer is that after her death, her corpse was arranged to look like she was still pregnant. According to the Star Wars Episode III: Visual Dictionary, her parents and sister were informed of her death but no further investigation (or official autopsy) was carried out on the planet due to Naboobian tradition.