Mr. Fitzsimmons is first seen while he is working at the school; we see him cheering Jimmy on as he fights Bill urging him to kick Bill's ass.
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. Frank angrily says that nobody calls his kids a psycho except him and demands an apology, Mr Fitzimmons sarcastically mocks Frank and says somebody went to college, Frank says he didn't go to college he went to Korea, Mr Fitzimmons tells him he should have stayed there, Sue tells him to mind his language, Mr Fitzsimmons ruddy tells Sue to mind her own business calling her a 'Nosey Fucking Bitch', which prompts the fight between the Fitzsimmons and Murphy's, which end when Mr. Fitzsimmons is nearly strangled by Skeeball and then hit in the stomach by Sue telling him and Jimmy to get the fuck off her lawn, The Fitzsimmons retreat yelling that the whole Murphy family is crazy.
In Season 2, Mr. Fitzsimmons is shown beating Jimmy with a belt and 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, likely passed out from drinking beer.
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.