I disagree with the theory that Buffy behaved in an immature manner by chasing a known threat to L.A. and then stepping all over Angel's territory.
First off, there was at that time supposed to be one slayer in all the world. She guards the Hellmouth because there's more demon activity there than anywhere else in the world -- L.A. included, not because it's some sort of playpen to L.A.'s real world badness. That said, there's one slayer in the world (as a rule). That pretty much means everywhere in the world is in her jurisdiction. As a vampire, Angel can't just carve out a piece and hang up a "No Slayer's Allowed" sign like it's a clubhouse and he's a boy who believes in girl cooties. He doesn't have that right. No beasty has that right. The slayer can come and go as she pleases.
Secondly, Angel was sticking his nose into a slayer problem, not the other way around. His intentions were good, but part of what was going on with Faith was a power dynamic between the two slayers. There was supposed to be one slayer. Instead, there were two. One went rogue even after attempts were made to recover her. Buffy was doing her duty in attempting to take out a dangerous element of the demon world and she was also restoring balance by removing the second slayer. She was angry and vengeful, yes, but she also had a point as well as every right to deal with the Faith problem. The Faith problem was Buffy's problem -- even moreso when Faith went after Buffy's family, body, and position as THE slayer. The facts that Angel wanted to help Faith and that she ended up in L.A. do not necessarily give Angel the right to interfere by telling Buffy what she can or cannot do and where she can or cannot do it.
Angel has no rights in this slayer/vampire thing. Buffy's the boss. Angel exists because she allows him to live. She makes an exception for his souled status just as, later, she makes an exception for Anya's changed nature, for Spike's chip, and for Clem's ability to assimilate. For him to assert any sort of rights over Buffy is ridiculous. He certainly has no right to hit her or to expel her from "his" town just because he doesn't like her policy regarding rogue slayers. I'm betting that if he wasn't her ex, his butt would have been dust for far less than that.
I think Angel was way out of line. He was asserting rights and control that he just plain didn't have.