As Shon suggested, the "three month" bit is probaby there because somebody thought, not unreasonably, that Spock needed at least a few months to recover from his death and get his mind back up to speed. It also gives Kirk a decent interval to mourn his son before diving into the light-hearted fun and games of TVH, which makes sense. It would have felt strange if Kirk was breezily flirting with Gillian Taylor over pizza just a few days or weeks after David's murder . . . .
As for why Starfleet didn't come after them, I figure:
1) Sarek pulled strings to grant them asylum, and
2) To be honest, Starfleet was probably not in a big hurry to arrest a hero like Kirk and put him on trial. Heck, I imagine Kirk and crew had a fair number of sympathizers in high places who were happy to let the Vulcans deal with them. I mean, it's not like Kirk and his crew were dangerous terrorists plotting against Earth or something. They had disobeyed orders and taken their ship on an unauthorized mission, which, granted, Starfleet could hardly ignore, but nobody thought they posed a threat to the Federation--or really wanted to embarrass Starfleet by putting its greatest hero through a very public court-martial.
"Darn! The Vulcans are protecting Kirk. What a shame. Oh well, I guess we won't be able to drag him back in chains this week . . . . "
As for why Starfleet didn't come after them, I figure:
1) Sarek pulled strings to grant them asylum, and
2) To be honest, Starfleet was probably not in a big hurry to arrest a hero like Kirk and put him on trial. Heck, I imagine Kirk and crew had a fair number of sympathizers in high places who were happy to let the Vulcans deal with them. I mean, it's not like Kirk and his crew were dangerous terrorists plotting against Earth or something. They had disobeyed orders and taken their ship on an unauthorized mission, which, granted, Starfleet could hardly ignore, but nobody thought they posed a threat to the Federation--or really wanted to embarrass Starfleet by putting its greatest hero through a very public court-martial.
"Darn! The Vulcans are protecting Kirk. What a shame. Oh well, I guess we won't be able to drag him back in chains this week . . . . "