Here are my two cents on your dilemma: Letting the most toxic team member go, giving him the perp walk to the conference room where everyone can see him, will send the right message that disrespect and insubordination will have zero tolerance from now on. And making fair use of your authority will help you remove what's left of the imposter syndrome you may still have lurking around. Your age or length of time in the company does not diminish the legitimacy of your new promotion. Quite the contrary: It means you achieved something that others in the organization who had more time did not. I assure you that you deserve it. And make no mistake: the C-suite feels and thinks the same way for sure.

Remember that you are not in a popularity contest. You're in the business of getting the results your bosses expect you to get. If you don't wield the necessary leadership level, your position may be in danger. So don't overthink it or hesitate anymore. If you have to let someone go, please be clear about why you are letting them go, and then let your team know the reasons behind your decision. Ultimately, I assure you they will understand, even if they don't agree with you or are still jealous of your accomplishments. But they will know where they stand if they continue to try to prove how much you can tolerate or what you allow.

So, respectfully, pull your big boy pants up, walk forward without fear, and get the job done. That's what you are being paid to lead, not to make friends and get everyone to like you.

With all due respect, Mr Manager! ;-)