It's not necessarily unreasonable. It depends on the specific situation you're in. Given that there's reason to believe he does not have the necessary equipment and supplies, it sounds fine. Under Court Rule 5:8-1, the Court, if mediation is unsuccessful at resolving custody issues, may "before final judgment or order require an investigation to be made by the Family Division of the character and fitness of the parties, the economic condition of the family, the financial ability of the party to pay alimony or support or both, and the parties' homes, which shall be limited to a factual description of the home where the child will reside or visit, appropriate child safety precautions in the home, number of household members and their relationship to the child, and criminal record checks for both parties."
Unfortunately, I do not have enough information to give you proper guidance without conducting a free consultation at my office in Somerville, NJ. There are too many questions left unanswered by a short description of your issue here on . If you're going to make this claim, I strongly suggest reaching out to a skilled custody attorney. He or she will be able to help you protect your rights and the rights of your child under the law.