Thank you for your question and your comments. Socialization can become more important as children become older. It is natural for them to want to reach out to the world. Some children may feel this more keenly than others, especially an only child or the last child to leave the nest. I think of Catherine of Siena who wanted to live a withdrawn life at home until she received the inspiration to go out into the world. She was ready to do so. God can be served in various ways.
Based upon the information in your email, you seem confident that your daughter may be ready to go out into the world as well. You know her best, and the whole point of home schooling is to do what is best for our children. Your daughter has already had some preparation for making the switch, and if she is agreeable, I would let her try it.
Not every middle school is the same, and schools can change rapidly depending upon changes in the administration. You will want to keep the lines of communication open between your daughter and yourself and between the school.
You should not be surprised to see some changes in her as the influences will probably work both ways. We cannot help being influenced by others and by changes in our environment, but at some point, your daughter will be out in the world and will need to understand differences in education, traditions, culture, and morality. She will need time to adapt, and you may wish to set some boundaries for her. While certain behavior may be acceptable or tolerable at school, you do not have to accept that behavior at home. For example, it is not uncommon for middle schoolers to whine, but you may make it clear that whining is not acceptable at home.
Switching to public school may be good for your daughter for a while or for the rest of her schooling. You can always switch back if serious issues arise. You can also supplement the public school program if necessary, but I would not overburden your daughter with extra work. Looking further into specific topics together or finding out what the Church has to say about issues together may be sufficient.
May God smile upon your family and grant you peace over your decision.