What the mediator can do, though, is assist the divorcing couple in formulating ideas that can eventually lead to agreements that will stand the test of time. That open and free exchange of information frees up both spouses to negotiate with each other in confidence. Because both spouses are working with the same base of information, it usually takes far less time to negotiate a resolution that makes sense to both spouses.
A trickier question is whether you may record the other parent's conversations with the children. Under the doctrine of "vicarious consent," as long as a parent or guardian has "a good faith, objectively reasonable belief that the interception of telephone conversations is necessary for the best interests of the children," then he may consent to the interception (i.e. listening in or recording the call) on behalf of the children.  However, this can be risky, because if there is any dispute about whether your vicarious consent was in good faith or objectively reasonable, you may still end up having to defend against possible criminal charges or a civil lawsuit. The Wagner case I have cited, for example, was a civil lawsuit by a one parent against the other parent who had recorded telephone calls between the children and herself. The Court allowed that lawsuit to proceed because there was a genuine issue of material fact as to the motivations of the parent who had made the recordings. I don't recommend recording any such phone calls without first consulting a lawyer.
The next step will be to assess where you and your spouse agree and where you need some work to get to agreement. Once you have a sense of what needs to be accomplished, you, your spouse, and the mediator will plan how you're going to accomplish it. It's very likely that you will need to gather more information, especially if you're dealing with property issues as well as child custody questions. (For example, if you don't know the value of your house, you can't have an intelligent discussion about a buyout.) The mediator will help you figure out what information you need and ask each of you to commit to bringing certain things for the next session.
When deciding which party to award a marital pet, a compelling argument is the pet’s attachment to the children. If there are minor children involved, who are very attached to the pet, the Court will likely award the pet to whichever parent has primary residence of the children. Another compelling argument is which party cares most for the pet. If you can prove that you were the one primarily responsible for feeding the pet, taking it to the vet, walking it, etcetera, then you will be much more likely to be awarded the pet.