Character-building is as much a part of homeschooling as Math or Reading. It's an integral part of parenting. Being with you all day, kids are bound to learn something valuable from you- seek out opportunities to put it into words.
If you notice someone being mistreated, help if you can, even if it's in speech alone, and then talk to your kids about why it happens and why it's wrong. Ask questions, get them thinking. One situation at a time, help them become responsible, compassionate, self-assured adults.
On the homeschool character-building agenda today: Teach my kids that "nothing other people do is because of you". Any actions or reactions you see of others stem from their own personal issues (or lack thereof) so disregard and excuse the naysayers, and gather strength from those that lift you up. Most of all, keep on truckin';-)