You are best served in any court - criminal, civil or family - if you are represented by an attorney. You don't want to be in the position of having to defend yourself or explain your actions or the disposition of the criminal matter to a judge. The case against you was dismissed, you were not convicted and thus you shouldn't really have to answer for this but the family court judge can properly inquire about all bad acts that potentially make you an unfit parent, whether such acts were proveable in criminal court or not. Again, a good attorney will put a stop to opposing counsel trying to suggest that you did something wrong or allow the judge to put you on the defensive. Hire counsel. If you really can't afford to hire an attorney, bring the last minute of your criminal matter to court and if the issue arises firmly tell the judge that you were innocent, the case was dismissed and that it is irrelevant and unfair for the court to consider this in its proceedings and then move on to more substantive issues. I would not go into the details of the charges or attempt to relitigate a case that has already been dismissed in your favor.
If she attempts to.. just explain that there was no factual basis for any arrest and the charges were never filed because your blood came back negative for any controlled substance. You should have an attorney help you - a Family law attorney.
Lawyers use whatever admissible evidence they can to be a zealous advocate for their client. That said If the case was dismissed it's not going to carry much weight. Also there has to be a showing of actual risk to the child. make sure you hire counsel custody issues are complex.