Is the husband entitled to read his wife’s text messages or emails, and when and how? And did the wife err by not allowing her husband to read her message?

The husband has the right to obedience and good companionship. However, the husband does not have the right to pry into his wife's private matters as long as she is free from suspicion, unless she asks for his advice. Therefore, it is appropriate for you to show your husband the message that caused the problem between you, even if it goes against the general rule. The benefit of reconciliation between you takes precedence over preserving this privacy. The problem is minor, so do not let it affect your home. Be patient with your husband, and do not inform him of your problems with your friends again.