As you have seen above many Orthodox Christians have chosen to Homeschool their children. The most common response I have heard about why is "To raise my children more fully holding an Orthodox World view rather than a secular world view that public schooling provides." It seems to shut up most critics.
If you haven't already, provide the Presbyterva with the name and website of your accredited school that provides your material and testing. I commend you for this, many Orthodox Homeschoolers forget this aspect of schooling---This shows the efforts you have made to go beyond what many homeschoolers have done, i.e. established a standard of excellence and measure of your child's achievement.
Most professional civil educators have a great concern that Home school kids while excelling in education, fall down is social graces and socialization. This is a myth held by most secular educators, in that many homeschoolers are members of local homeschool associations that arrange play days for younger children, encourage participation in community sports (football, soccer, basket ball) and in some larger communities even have established bands and orchestras for the children. A local one near where I live has a science lab taught by parents with appropriate degrees at a community college to give lab experience to high school age members of the co-op. Beyond this often these children are very active in the Orthodox Church youth groups and scouting, Brownies, Campfire, Civil Airpatrol etc. These all offer excellent opportunities for home schoolers to socialize.
As always, if this is an issue, meet with your Orthodox priest to discuss the issue. I have know priests who will ask their wife to back off, remember his has the charisms give at ordination to pastor you, his wife does not.
Corrected for spelling - Thomas