I think homeschooling it the best option, especially since your daughter is being bullied. I think what happens in schools is that they learn from their peers - and as you are seeing they are learning how not to behave.

As far as socialization, I know in many US towns there are homeschool groups where children can come together to do things like sports or arts for interaction. I've taught several home school children music, and you would never know they were homeschooled due to how well they interact and how mature they are.

So enroll them in some after-school activities for the social aspect, but having them home where they seem happier is a great decision.