Sora, Riku, and Kairi were right in the middle of the storm/ attack when the heartless came and destroyed the island so it probably never crossed Sora's mind to search for "supposedly-safe-at-home" family members. I don't think they realized at first that Destiny Islands was destroyed.
And many people trust friends more than their parents; there's plenty of stuff one can trust a best friend with rather than a parent; so maybe Sora doesn't care as much for his parents..?(I know plenty of people like that, although Sora probably loves his parents plenty)
Also, you notice we hear no more than 3-5 words from his mother, and we never see either of his parents, so maybe they were just trying to not make the parents very important to the plot ; and the voice calling him down to dinner didn't have to be his mom~it could have been an aunt, or an older sister...etc.
It seems to me that they were trying to make the family concept as vague as possible.