Tell them what you've just said here.
Most judges will roll their eyes when they hear "I honestly didn't realize" or similar. Usually one isolated incident won't result in anything overly nasty, but put together with the letter issue your ex might actually get lucky and have you held in contempt as it almost - almost - suggests you're trying to push Dad out a little.
Now that won't change custody at this early stage, so don't worry. But it will be on record, and you'll need to keep your nose squeaky clean from hereon out.
Going back to the privacy issue. Mom, your rights weren't violated at all here - in fact, it wasn't even you the paperwork concerned but your mutual child. You have very little personal privacy where your mutual child is concerned.
You really had no right to refuse Dad the information (although he could have found out himself).
So when you get to court, apologize politely and sincerely for the errors, and point out that you did offer to bring kiddo to Dad IMMEDIATELY after the appointment but Dad refused.
Have you guys taken any co-parenting classes, out of interest?