Hi and welcome. It's great to read a bit about your thoughts and experiences with homeschooling. I think you'll find we all have worries about whether we are capable enough to teach our children, but the fact that your wife has already realised their learning styles shows you how a parent's input in their child's education is beneficial. Different learning styles can't always be catered for in big classrooms. Also the fact that you are both engineers tells me that you are both well educated and therefore capable of passing knowledge on. While a background in teaching means you will have a more in depth knowledge on education, it is still a modern phenomenon that we train teachers. For thousands of years we taught our children without officiously trained teachers, so your input and the input of those other trusted ones around them is still valid.

I must admit that because of the fear of the pandemic we have not exposed the children to other people and this has brought as a consequence that they feel fear when they are with other people

That is a concerning aspect of these last couple of years, especially for young children who have little experience of anything else. I hope you can continue help them to gain confidence around others again.