Well, there's actually a lot to choose from.
Spock and Sarek didn't talk for nearly 20 years because of a disagreement of career choice. This was added to issues of acceptance because his half-human son apparently carried too many traits of his mother's ethnicity.
Bashier's dad had an illegal medical procedure performed on his son, resulting in shame from Julian, and later imprisonment for dad.
McCoy had an unhappy divorce, separating him also from his daughter, from whom he seemed to be practically estranged.
Sulu was an absentee dad.
Picard also had a cold relationship with his father, and was constantly at odds with his brother. Neither dad nor brother accept or respect his career choice. He then loses said brother and nephew in a fire.
Sisko's mother was actually an alien who possessed a woman who left his dad after he was born. He is raised by a woman who he thinks is his mother, and his father doesn't fill him in until years later when the issue is basically forced. He, of course is widowed with a young son to raise.
Deanna's mom is just a royal pain in the ass, and had lost a child, never telling Deanna that she had an older sister who died.
How's that for starters? I don't know who I'd pick. Probably Spock.