Your narrative is a bit difficult to understand, I'm afraid. (Please see this Guide: http://www.avvo.com/legal-guides/ugc/five-tips-for-how-to-ask-for-legal-advice-on-avvocom .) But here is how this works in general:
A custody agreement is enforceable once the parties have stated on the record that they agree to it and a judge has ruled that it is in effect. When that happens, if one or more of the parties has a lawyer, one of the lawyers is assigned to draft a judgment that reflects the agreement and submit it to the judge for signature. They're required to let the other side review their draft first, to be sure that it accurately reflects the agreement recited on the record. If they can't agree, then they can ask the Court to hold a hearing to determine how the judgment should be written. The real trouble can come if a party wants to enforce the agreement before it's been memorialized in a judgment and signed by a judge. In theory this is possible, but I have seen some judges claim that because there is no signed judgment, there's nothing to enforce.
If neither party has a lawyer, then the court is not going to order either of them to draft this "form of order;" rather, the judge will generally do it themselves, on the spot. This can avoid the problem of that limbo period where there's an agreement on the record, but no judgment.
It's not quite clear to me from the question whether you actually agree with the terms in this mediated agreement, or not. If you don't agree - taking into account the risk that your outcome might be worse if you take the case to trial - then you shouldn't sign it. I would recommend not signing anything until you've had it reviewed by your own attorney in private. If you sign it, you are agreeing with all parts of it, not just the parts that you like, which seems like a concern.
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