What are some ways to describe the fathers way of being in the story?

Malachi McCourt Sr. is the patriarch of the McCourt family, Malachi is an alcoholic who remains unemployed most of the time and spends his salary at the pub when he does have a job to the despair of his wife and children.

So, you need to find three solid points that define this guy. In your thesis statement, begin with the general then move to your specific points. For a thesis you might consider,

"Malachy McCourt Sr.is the father of the family. Although he shows affection for his family, particularly for his sons, he has many debilitating issues which affect both him and his family."