If the player isn't having fun with his character, why isn't he allowed to switch?

I'd be happy if he wanted to switch, but he really wants to play a LG Cleric because he finds my pantheon interesting, and he seems interested in starting a religion of his own based around virtues rather than aspects.

With a person who hates him, and three people who are complacent

Definitely a composition problem here, but I'm leaning more toward the CN being the problem, not the LG. I can work with the LG. I can pander to him, but I just have no fucking clue how to play toward Patches and get him hooked to the party. I'm absolutely failing to figure out this PC's motivations and what it'll take to get him to stop fucking with the Cleric. If we hit another few sessions and my attempts to reform Patches into a workable party member aren't working, I'm really considering pulling out the stops and putting Patches into the dirt. A tally is being kept, and I've started the process of shrinking the ground from under him, including turning the entire party against patches right at the end of the session. I'm going to send him a message to let him know that PC-PC action is ill advised. Either IC, or if this carries into next session, OOC under the table before the session's over.

Of course, the problem now is that you've locked him into a character he hates playing for at least the next session until the situation which is "absolutely not be possible for the party without a cleric of his specific skillset" rolls over.

I'm really trying to get the Cleric involved in something he's going to appreciate. He's voiced his concern, and I'm struggling to find an ideal way to meet that concern. I really just want my PCs to ultimately be happy, but it's becoming clear that if the Cleric's unhappy, Patches is ecstatic, and if Patches is unhappy, the Cleric's ecstatic.

The solution is absolutely NOT canning a volatile player. The solution is NOT forcing a player out of their role. The solution is attempting to forge a bond between these two players and making them reach a place of mutual respect, if friendship isn't achievable.