child custody. should i submit a rebuttle to her allegations. .

Normally, you would want your side of the story, and any evidence relevant, to be part of the court file so if mediation fails and you are back before a judge, the filings give the court something to consider in your favor.  If you feel that there is some reason you should not disclose what you know about the issues, you really should go over both strategy and tactics with a family law attorney.