This is a very thoughtful question. I especially liked the way you described a child's holistic development. This is insightful and one of the main reasons that parents choose to embrace the homeschooling lifestyle. Holistic refers to the interconnectedness of all things. In the case of a child's development this would mean the interconnectedness of all aspects of a child's being. Naturally this would mean that as parents we are taking into account the spiritual, physical, mental, and emotional well being of our children. It would mean that each one of these important areas is very much connected to the other. This being true, then it is also true that to develop fully is to consider the part that each of these areas plays in the development of the other. For example, what is the worth of academics without the realization of the gift of intelligence and the part that spirituality plays in this realization?
School systems are not supposed to develop all these aspects in the child. This is not their function. A school system strives for this ideal however their main focus is academics. If holistic attitudes were a mandate in the school system then it would stand to reason that having parental involvement would be at least one part of that mandate. Though school systems will tell you that parental involvement is vital, they are not in the position to require such involvement. So too school systems can not mandate that a child be developed spiritually. However if one believes in the holistic approach of child development then this is one aspect that would have to go wanting. There are many that feel school systems should not be involved in all areas of a child's development for in so doing their own agenda would be implemented. Suppose this agenda involved disciplines that were contrary to a family's particular faith belief? To discredit a family's faith belief is then to interrupt the holistic education of the child.
Does all this sound complicated? It isn't really.
The parent is the most ideal person to determine the holistic development of their children. The parent is the one responsible for the total well being of the child in that they are the only ones who have that authority by very nature of their parenthood. Parents must answer for the development of their child by the standard that is set in their reference of maturity. I would not want an outsider determining if my child were mature enough to view a movie that I felt was beyond the child's years. In the same respect let me ask you another question.
Is the goal of parenting to mature our children by the standard set by those who do not know or even love our child? Each parent must answer for their parenting and in so doing they must bear the responsibility for the actions they take or neglect to take. For example, to neglect to tell a young person about the dangers of swimming in unguarded areas is to neglect to help the child make an informed choice when faced with this decision.
The Catholic homeschooling lifestyle in particular takes into account the interconnectedness of all aspects of a child's development with regards to all areas of development. Certainly to focus too much on one aspect without provocation is to create a sense of imbalance in our parenting. When humans are in a state of imbalance then the likelihood they will feel tension, stress, and compromise is very real. For example, to neglect to tell a child about the goodness of Jesus and His great love for us is to lessen a child's true knowledge.
Socialization issues are very real challenges that all parents face. It is untrue to think that only parents who choose to homeschool must face this very real challenge. I would think that all loving parents would be concerned about the amount and type of socialization their child receives. This is an issue that plays a role in parenting and will continue to play a role as long as there are children who want to 'play with somebody' their own age. Perhaps and at times a homeschooling parent will have to be more creative in their efforts but this is not above what any parent who desires a holistic approach to parenting would want as well.
Your child is very blest. She has in you a seeker and a searcher. This is wonderful. When we explore our options, responses, and actions we are opening ourselves up to the direction of the Holy Spirit. In giving us the opportunity to parent the dear Jesus has also given us the heart and the mind to put our children first and to direct our efforts to this end. The most important aspect of parenting is to allow the Holy Spirit to guide every aspect of our parenting. Through prayer, the Sacraments (in particular Reconciliation and Holy Eucharist), our interactions with persons the Lord sends our way, and many other opportunities He sends, we are better able to hear His directive and follow along the path that best suits our child. Jesus deals with each of us singularly. Our relationship is intimate and personal, therefore we must be open to what we hear the Lord tells us to do for our situation. Keep praying and keep searching and researching. God love you. Praise the Lord for the gift of motherhood and the power of His Holy Spirit.
Let us pray together a Hail Mary for all mothers. Jesus, we ask that You empower moms to hear Your call upon their efforts. Amen.
Sending out a prayer,