Yes. An FBI agent has no legal authority to order you to do anything; a judge does. That said, it seems unlikely that a judge would order you to interfere with an FBI investigation. If there's been a ruling on this, you need to hire a lawyer and see about filing a motion for reconsideration, or, failing that, getting a protective order. If the FBI guy is serious about this, they should be willing to back you up and tell the judge why he wants you to not answer this. (I'm assuming that you've been unrepresented so far. If you have a lawyer, you need to ask them this question, not some strangers on the internet. They're bound to know your case better than we can.)
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You have to do what the judge orders you to do, or risk being held in contempt of court. And I'm not sure how this would be grounds for a mistrial or any "form of relief" to you, because I'm not sure how you (or your case) would have been harmed by being asked to answer a question about the FBI. If you have an attorney already, you should be asking her/him about this.
It seems to me unlikely that this could have any impact on the custody matter. The cat's now out of the bag -- the other party knows at least that the FBI is involved in some sort of investigation -- and that may jeopardize the investigation, but that's a separate matter from your custody dispute.
If there's a possibility that you could be questioned further on this, and that additional answers could harm the FBI investigation, then the normal thing would be for the FBI agent to involve the U.S. Attorney's office to seek a protective order against the questioning.
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