Your family could require a judge to admit you for a psychiatric assessment but it is the psychiatrist whose opinion matters, not your family's. If you are not considered a danger to yourself or others you would be discharged and sent home after the psych assessment. You don't lose any rights for an evaluation.

You do lose some rights if after the evaluation the pdoc advises to admit you to a state psychiatric hospital for extended treatment but that is uncommon and you sound much too stable to require that.