“The other side have been messing me around for nearly a year, so I am determined that they will take me seriously when bargaining towards a settlement in the mediation. Can I rely on you to make it clear to them what my bottom line is?”
No, it is very unlikely I would ever to this. If I do it will only be following a direct instruction from you. It is not the way that I (or any competent mediator) would use the process. To be taken seriously you can simply reject their insufficient offers and make reasonable counteroffers of your own, using me to provide your reasoning.
Bear in mind that your bottom line is only the least that you can tolerate accepting form the other side. Your efforts will aim to reach an agreement that contains more value than that. If I reveal your bottom line the other side will never offer you anything better, and I would be damaging your interests.