You absolutely can reach a willing agreement by making full use of the process and of me, regardless of how this person behaves. These points will make you feel better:
(1) In the safety of your private sessions, you will not be seeing or hearing this person.
(2) This person’s lawyers have a duty to promote that person’s best interests. In most mediations that means settling. If the strength of personality is hampering that process, they must take steps to quieten it down.
(3) I too have a contractual duty to apply care and skill to promoting a settlement. I will take my own steps, with as much forceful courtesy as needed, to modify this person’s behaviour towards the outcome of settlement. I also do this with flamboyant lawyers, who sometimes need reminding that they are not in court and I am not a judge.