Honestly from what I have read you have only two options.
1. Kick the raid leader of core 2, anyone who mouths off remove them as well. Also kick the hunter, anyone who thinks that taking advantage of someone's kindness or being naive is a complete utter peice of %#$@ and should treated like one as is anyone who condones the action.
2. Try to work things out when they have openly broken the rules and defied your authority, going down this path things will become messier, and core 2 will either leave if you are lucky or destroy your guild.
The bottom line is this, Guilds are not democracies, there is one GM and what that person says goes, if they dont want to listen or like it, fine there is the door. You have already set a precedent that anyone can challenge your authority with no repercussion, you need to swiftly slam that shut or things will get out of hand. It is not always easy but the bottom line is it's 1 guild no matter the raid teams/pvp teams/non raiding members within it, which means 1 set of rules, and 1 leader. Clearly they have no respect for your authority so there is no reason for them to be in the guild, they basically have said we dont care about the guild we care about our 10. You need to say, I care only about my guild and resolve the issue.