Did I err when I prevented my wife from going to her family without my permission, and is her going without my permission considered a wrong action?

If the situation is as you have described, then your wife is obligated to obey you, and she should not have gone to her family without your permission. It is incumbent upon her to return to your home and treat you with kindness. Her brother has no right to prevent her from speaking with you, and she must obey you in returning home and treating you with kindness.