Mr. Fitzsimmons is first seen while he is working at the school; we see him cheering Jimmy on as he fights Bill.
The second time is when he picks a fight with the Murphy's over Jimmy's black eye. He believes Jimmy's story that Bill was trying to force him to rob the church, and this is probably supported by the fact that when he saw Jimmy and Bill fighting at school Bill started it by sucker punching him. Like his son, he is generally rude and un-empathetic as seen when he insulted Frank and called Sue a bitch in front of their kids. Also when he sprayed cleaning product in Phillip's face to stop him from cheering on Bill.
In Season 2, Mr. Fitzsimmons is shown dragging Jimmy to catholic military school when he's told about the shoplifting, and again when he's picking Jimmy up. He makes a brief cameo in his home during the finale, where he's sleeping on the couch in the background.