That's another of the unwritten rules of moderation, I think: You WILL get flak. There is no scenario where you get no flak. Therefore, you must not treat not getting flak as an end goal, or you might as well just turn the moderation power over to your biggest assholes and cut out the stressful process of being the middleman for their asshole decisions.
The question for a moderator is, who is giving you the flak? If it's the sort of people you don't want in your community, whoever that may be for your community, then you seem to be on the right track.
A private message to the mods from an asshole pulling every psych trick out of the book to hurt you in that private message is not a sign of failure; it is a sign of success. It can take a bit of emotional adjustment to feel that as a success and not a failure, but it's doable. The more vicious they are in that post the more they are proving you didn't want the there anyhow.
The question for a moderator is, who is giving you the flak? If it's the sort of people you don't want in your community, whoever that may be for your community, then you seem to be on the right track.
A private message to the mods from an asshole pulling every psych trick out of the book to hurt you in that private message is not a sign of failure; it is a sign of success. It can take a bit of emotional adjustment to feel that as a success and not a failure, but it's doable. The more vicious they are in that post the more they are proving you didn't want the there anyhow.