My children we always homeschooled. I never sent them to school.
We were involved in church, but mainly my children socialized with adults. They were very comfortable visiting the elderly in assisted living and chatting with them. Some became great friends and a grieving process when they died. But that's life.
When we had friends over (we became parents later in life, so our friends had older children), our children would love to sit with us and chat. Our friends loved our children, and each of our children had one friend of ours who became very special to them - they just clicked.
There were also piano lessons. Another homeschool mom gave them and so as they took turns with their lessons, they played with the other family's children.
There were a few other homeschooling families we would get together with and do trips to the zoo or museums, and for a while we all helped cleaning our church's sanctuary when they were temporarily without a janitor.
Also, when you have four children, there is socializing going on!
However, I much preferred my children learning their social skills from adults rather than their peers. My children thought many things other children did very silly.
My children, starting when they were young teens, were sought after by others to help with babysitting and helping them. They were mature enough to be the first ones they asked.
I don't know about your laws there for homeschooling, but it could be a possibility with your mother that it could be considered a private school. Not sure.