So one question I have for is if you are meeting with a lawyer, or meeting with a mediator. A mediator can be a lawyer, but not your lawyer. If you haven't met with someone with regards to your interests, you should do so before you agree to anything with a mediator. The mediator has one job - try to settle the case. They aren't looking out for your interests, or your wife's interests. They may give you some general information if neither of you are represented, but they shouldn't give you any advice outside of how to settle the case.
The age of your kids may still matter. I'm licensed in Oregon, so I'm not sure what the rules are here, but most states have an age at which parents aren't required to support their children, whether they are in school or not. If support is required for them, that's usually handled through child support - sometimes paid to the spouse that is mostly in charge of them and sometimes paid directly to the child. If it's paid directly to the child, that means that both of you would likely have an obligation.