Absolutely! One of the most cherished constitutional rights we have is the right to a public jury trial where anyone can witness the court's proceedings, as opposed to a closed tribunal where proceedings are held in secret.
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A criminal trial is a public proceeding. Unless there are specific orders by a judge about who can and cannot attend a trial or criminal proceeding, ANY member of the public can attend a court hearing, and their immigration status has no effect on that right.
The short answer is yes, family can be in the court room since the court proceedings are usually public. That said there are exceptions to this. One such exception would be when one the family members is a foreseeable witness at which point he or she is likely to be excluded so as not to bias his or her testimony.