I had the same problem this past spring. I used Nice Wildlife Service. It was $1000 total ($600 to trap, $200 to spray something that neutralizes the pheromones and sanitizes the area, and $200 to seal the hole). The fix is warrantied for two years.

They tried non-lethal traps at first, but the squirrels kept avoiding them. They took out the father squirrel with a pellet gun, and the mother ran away. They sealed the hole, and the mother was not able to get back in, thankfully. She did come back and had babies in the pine trees behind my house. The hawks have gotten the population down to one...