First, if you are both not represented by legal counsel you will need to have your signatures notarized. Second, you may use the FL-355 to modify the current order. You can always attach a very detailed list of the times/dates, etc. Once the form is signed (notarized), submit it to the clerk for the judge's signature. Once signed, then file with the Court. Remember to make sufficient copies so that each of you has a copy. Your instinct to make the agreement into an enforceable order is a...
The Family Court is, in theory, gender blind. The right to have a relationship with either parent belongs to the child, not the parent. The Court is going to look at the entier picture to determine what is in the best interests of the child. It is doubtful, based on what you say, that the Court will immediately grant mother unsupervised, shared custody. They will err on the side of caution. It is also possible, however, that if mother proves herself to be able, her visits with the child...