The choices your daughter has made to be alone with this boy are concerning and go beyond interest in the opposite sex that is typical at this age. It might be that the meetings were the boy’s idea or that she even felt pressured to meet with him. But ultimately, she made the choice too.
Lack of maturity and insecurity may be playing a part in this situation, but the fact that he is telling her who she can and cannot talk to indicates he is a controller. This is not a trait you want to see in a guy to whom your daughter is attracted.
Too much privacy for a young couple at this age is dangerous. It puts individuals in a compromising position and tempts them to engage in physical/sexual activities that are difficult to resist during the hormone-driven teen years. The fact that she participated in risky behavior at school and snuck out of the house raises safety issues as well.
You sent a strong message to her by moving her away for a while. Do you have a date for her return? You and her father need to be on the same page and present a united front on whatever you decide. Disruptions in the school year and social agendas can be pretty tough on kids. She may be truly sorry for her behavior and really may not want to see the boy again. But it would be wise to set some very specific house rules and expectations in regard to her relationships when she returns. You can even talk about future consequences if she breaks these rules.
It will be necessary to change the rules or add new ones as she gets older. For example, a 13-year-old child probably does not need specific rules about driving a car, but at 15, some very specific rules on curfew, seatbelt use, and the number of passengers allowed in the car should be discussed and agreed upon before the child can actually drive.
Your trust in your daughter will have to be rebuilt, and her actions and good behavior will help start that process. But it takes time to heal wounds once trust is broken. When she returns home to your care, let her gradually restart her social life by letting her have a few privileges at a time. Eventually, she can earn the privilege to go out with a group of friends to a movie or a school activity. How much freedom she regains is really in her hands. Be sure to praise her when you see her behavior improve or when she makes good choices.
We all make mistakes. Look at the mistakes your daughter makes as opportunities to teach her positive skills and strengthen your relationship.
