At some point prior to Treasure Planet, Leland married Sarah and some time later had a boy named Jim on the planet Montressor. When Jim was still young, his father left the planet for unknown reasons leaving his wife and son without support. He possibly left because he couldn't handle the responsibility of a father and a husband, he could have left because he wanted to see the galaxy or he left to seek a means to provide a better life for his family.
After he left, Sarah had since having problems with raising Jim who had grown into a carefree and problematic teenager due to lacking a role model.
Both left their wives and young sons in order to find a better life for the poverty-stricken family.
Although his name is not mentioned in the movie, it is shown in the Treasure Planet art book that it is Leland Hawkins.
According to notes in Treasure Planet: a Voyage of Discovery, Leland was nineteen and Sarah possibly seventeen when Jim came into existence. The addendum that he arrived "sooner than either parent planned" could imply that Jim was conceived earlier in Sarah and Leland's marriage than expected, or was the result of indiscretion, a love child, and the premise for the marriage. While it lends itself to both predicaments, the latter can be corroborated by the note that Leland was "immature and not ready for marriage" nor "prepared to raise a family"; he "felt trapped in the commitment that being a part of a family requires and couldn't handle the responsibility of raising a child." It's possible Leland married Sarah out of obligation or was forced; either way, to salvage her honor (if 18th century tenets apply in TP's world, being pregnant and unmarried would've condemned her the same as in real society).