Your children are unique , with their own interests, strengths, and weaknesses. If you didn't revel in their individual personalities, you probably wouldn't be homeschooling. Instead of studying Greco-Roman history in sixth and tenth grades, you can study it every year or whenever you want, explore those aspects that interest your children, ignore those that don't, you can even do entire units on times and places glossed over in text books.
Events in Classical History happened roughly between the years 1000BC and 500 A.D. in the geographic area surrounding the Mediterranean Sea. The sequence and location of ancient events can be confusing. You may not remember whether Macedonian Alexander's conquest of most of the "known" world happened before or after the Romans won the Punic Wars, but this needn't be a problem. Because you're on the Internet, you can keep one window open to a map, and another to a timeline for guidance through your travels.
The timeline on the left is heavily skewed toward military or political events, as such it is traditional, dealing with themes of war, murder, -- generally in less concentrated doses than our daily news fare -- power, glory, heroism, and courage. It's easier to find facts to flesh it out than a timeline focusing on the arts. But a timeline of the major philosophers, dramatists, and sculptors would be more suited to many children and could contain more meaty reading material.
Besides tailoring your learning materials to your tastes and your children's interests, homeschoolers have a wonderful opportunity to take advantage of off-season rates for travel around the country or world. Even if you can't get to Greece and Italy to visit the actual physical spaces where our ancestors (intellectual, or otherwise) lived, breathed, argued, and watched the gladiators, Paris, London, New York, and many other cities house museums with excellent, attractive, and detailed collections of Greco-Roman art. It's important to remember that those great jugs (amphorae) you see with the legend about painter and red-figure or black-figure refer to vessels that were used for storing the food of daily life. That helmet may have saved the life of a now long dead hoplite and that perfectly proportioned statue of Apollo or Venus was modeled on a flesh and blood man or woman. Even if you can't afford to travel, the Internet offers two dimensional images of ancient artifacts.
The ancients did not live, believe, and behave exactly as we do. Sometimes their reactions are puzzling. Sometimes explanations are so pat, no one gives much thought to what they really mean -- until your young ones start asking probing questions. Then one of the bulletin boards for ancient history might be the ticket for your family.