Hi chatpandore,
Interesting and difficult situation. Most important thing is to remember that the attacker doesn't attack your sieges but he attacks your nerves, with quite success.
You clearly have the hardest position in this dual conflict with the other player. He can do to your sieges whatever and whenever he wants and you are limited since you are hegemon, in small coalition, and with many sieges.
Didn't understand the comment "Impossible for me to go on with my team", it is your personal problem not the problem of the coalition you manage and you should handle your personal problems without this affecting your ability to manage your team.
Also didn't understand Katia comment "we own only our city ", if a player attacks a city every day, not a siege but active city, theoretically it is allowed, so even our own city we cannot protect from multiple attacks.
Your wish to keep many sieges is also like saying "I want to keep several emporias for my personal usage", or "I want to keep several pans for my personal usage".
I looked in the screenshots and observed 2 things. One your sieges are mainly bot cities and not former active players, this ones have special raiding focus in sparta and i hardly see some with active sieges since they are more raided. Second thing, the attacked raids lines of bot cities, meaning he doesn't have extra time in game to spend on raids but many of his raids are in a time period of 5 minutes, the player has better things to do with his time in game or outside the game.
It is hard for you to prevent the attacks. Speak with the hegemon of his coalition, if the attacker is in bigger coalition usually people are morally good and the hegemon will help you or at least ignore your retaliation on him. If he is in a coalition on your size, you can target his entire coalition.
Another thing you can do, each sieges attacks on you, you attack, spy, or pa the attacker with small troops. If your spy told you he left his offence in his city you know what to do.
Another option is that you can have sieges far from your city so he will not find them. You can also trap all his attacks by learning his attacks and keeping just the troops to win his initial raids. You can focus on few sieges and defend them heavily and see his reaction of what he will do. You said he also attacks the cities of your coalition, you can defend them more easily.
By the way, I personally do not have active sieges and even rarely raiding empty cities.