Thank you for bringing this question to this forum. I think that it is timely and one that bears addressing as there many moms who have the same concerns that you have expressed.
It is apparent from your letter that you are a gifted and holy teacher who has a heart for children. This is an anointing from the Lord. To teach is to desire to bring those under our care and influence closer to their full potential and ultimately through this goal realize their vocation. However we also must realize that each child has within a certain amount of challenge that is used by the Lord to bring the soul to Heaven. We are created out of love, to love and to return to the source of all love, God Our Father. Our goal as teachers, parents, Christians, and humans is to help each one that the Lord places in our path to live within the Lord's will.
To be able to teach with a peaceful and fruitful attitude one must have a desire within oneself to follow the Lord's will. If after prayer and discernment you feel called to begin homeschooling your dear children, then you must begin. Your journey to Heaven is ultimately affected by your desire to follow the Lord's will. When we are not in accordance with the Lord's will for us, we have an absence of peace in our lives. Our efforts seem empty and parched. We work just to work without the peace that makes challenges doable.
Certainly the teachers in the Catholic school that you are now teaching in, believe that they too must follow the Lord's will in all matters. What man desires of us is pale and empty in comparison to what the Lord desires of us. Jesus desires that we journey to Him through our daily lives. What could be more simple?
I would imagine that the support of the Catholic church/school ultimately lies within the heart of each parish member. Sometimes financially sound parishes are anemic in effort and vexed in attitude because there seems to be a lack of the true understanding of the great gift that is possible through the holy Mass. To have a heart that longs for Jesus and desires to encounter His power through the reception of the Sacraments is a great blessing. The graces made available through a parish life that is centered upon the Lord and His sacraments are without measure.
Continue to pray about your choice. Remember that we are talking about two different issues. Perhaps you are being called to homeschool your children yet you are still in the process of discernment. You are trying to discern whether homeschooling is the Lord's will for you. Where your children receive their education is bound up in how you understand the Lord's will for your family. If homeschooling were not your calling then sending your children to a suitable and holy Catholic school would be understandable.
Let us pray together a Hail Mary for all teachers as they work through the many challenges that face classrooms each day. Lord we ask that you anoint their efforts and through the Holy Spirit empower and inspire teachers to first bring their students to the knowledge of the Lord and His great love for each person. Amen.
Sending out a prayer,