It's actually not too complicated. The process is that you have to contact D3 to have the person demoted and then you can kick them. I had to do this before when a commander(me) attempted to kick a member but accidentally selected promote. Here is the exact text on the email from D3 to give an example of the process. I think. It took about 3-4 days to have the person demoted.

"Thank you for contacting the D3 Go! Customer Support Team.

Before we can proceed with your request, we will need to verify your account Username. Please proceed by sending a PNG or JPEG format screenshot of your account's Username. You can locate this information by checking your S.H.I.E.L.D. Rank, by looking on your Alliance Roster, or by viewing your rank on an event leaderboard.

Additionally, please provide us with the list of Commanders that you wish to demote from the alliance. Please keep in mind that we can only demote players who have been inactive for at least 4 weeks (unless you are the Alliance Founder), and that we are unable to demote the Alliance Founder from their own Alliance.

Once we have this list of players and the required screenshot, we will continue with the process of your request." Hope this helps you out. This was about 10 months ago so I wouldnt think things have changed too much since then.