I've been thinking about this, and I'm not sure if any family members have actually been in court, as members of the public and not in roles as Ministry officials. Harry's trial was brought forward unexpectantly so he had no support to speak of from friends, etc. This gives you an opportunity to expand on what we know of a courtroom's layout and those present outside of official personnel and those on trial, but getting back to your question, if you are following the stylistics of a typical criminal case in our world, then yes, there is nothing to stop a witness discussing their evidence with other members of the public, family, whoever, once they have been freed from being a witness in a case - it isn't particularly advisable however, because you could be in a corridor discussing your evidence with person A, who might be overheard by person B who might know witness X who hasn't yet given evidence and may pass the information on if a situation came to be where the trial was adjourned for the night, although some cases, if they are important, have been known to run into the evening - the passing of that kind of information could potentially prevent problems with their evidence, although it would add a lot of pressure to a witness, who in the middle of a trial suddenly adds/omits information that was in their original statement, .
Would the prosecutor, if the family was a witness, then was told that they were free to go, then they stayed for the trial and watched--- would they be able to talk about it freely with them? I don't think that I was very clear either.
We know that the chains on the chair in court binds the accused if they are considered to be dangerous. In a room full of Ministry officials chances of escape could be difficult. So your 3 DEs, even if they are very accomplished wizards would do well to escape - I'm sure there would be plenty of counter measures in place, but an Auror or two preventing people from entering the court once a trial is underway would seem a very likely event, if there were cause for concern - they (be it Aurors or otherwise) would likely be the equivalent to our Group 4 prisoner custody officers (basically the Prison Service use contractors to escort prisoners/people remanded in custody from where they're being held to courts and back) - they use these to free up police and prison officers.
I understand that an Auror would most likely not be the best person to use, but would it be suitable for an Auror to guard the doors, if, say, it was three Death Eaters on trial? In case that they attempted some form of escape, for precautionary, high security reasons?