Some stories are epic and not so well told (cf Troy, Van Helsing) and some are intimate and very well told. House of Sand and Fog is a very small, even prosaic, story about two people who are driven by financial circumstance and their own flawed characters into conflict with one another. They draw into their struggle those around them, their family and acquaintances-cum-lovers, with tragic consequences.
When I think about what motivates the characters I think it comes down to prejudice - the immigrants' views of Americans and vice versa - and also pride. Both the the benefits and downsides of pride - in one's home and one's accomplishments - are shown.
All of the characters are finely drawn, in proportion to their weight in the story, with the exception of the son who I think lacked the proper attention given his critical actions late in the movie. The performances by Connelly and Kingsley are particularly praiseworthy - both have scenes where they need to show restraint and where they need to emote to devastating effect.
A good character-driven narrative because, with the possible exception of the deputy sheriff, there are no villains in this movie and certainly no heroes. Only people.