Mediation in CA is mandatory, but settlement in mediation is not. The mediator's job is to try to bring the two of you to a settlement, and report that settlement out, if it occurs.
If both parents are seeking the identical change in their favor, then mediation is a waste of time. Present your position and your evidence if you like and then just stand your ground and get ready to go to trial.
Alternatively, if you are certain in advance that the other party will not budge, then simply present your position without any evidence (no sense in giving your opponent a head's up on what you intend to present), and then just smile and state that you will have to discuss the matter with counsel -- eventually the mediator will simply say that it's obvious that the parties are too estranged for mediation to produce a meaningful outcome and the mediator will recommed to the court that a trial be held.
Based on your facts, I would be attempting to maintain 50/50, not trying to get more, and it sounds as though that's where you're gonna end up when the dust settles, anyway.