Why did it really matter so much to that Commissioner Pat Webb that his brother in law was fired?

People are always looking out for dimwitted relatives especially if kids are involved. I would imagine that LV is quite shallow in terms of employment opportunities. There is the entertainment industry and there is cleaning up horse plus cow crap. Cleaning up crap is more mechanized (few people needed) and does not come with a retirement plan typically.

I view it as all about power.

Webb forces the casino to hire useless relatives like Don as a flex, a way to remind the casinos who's in charge in that town.

And Ace's inflexibility is a counter-flex, to flaunt his own authority by refusing to cooperate.

It was a dumb move by Ace, but far from his only mistake in the film. That's the tragedy of it all, how "street guys like us managed to fuck it all up"

Because Mr. Rothstein never could understand the way it works out there. They were all just guests, but they acted like they were at home. Let Pat Webb tell you something, partner: they ain't home, but that's where they were gonna send them if it hareliped the Governor.