Trying to get joint custody

Currently mom has physical custody w/ father having visitation and he would like more custody - joint. We think we have enough “changed circumstances” to warrant this and can make a good case for having the children with us more. We live in the same school district. We have tried reaching an agreement w/ ex without success. I guess our next route is mediation, though I suspect this will also be a difficult if not impossible situation. What should we be preparing, gathering or be prepared for during mediation or court?