I think some of DD's unhappiness is directly related to seeing her brother being homeschooled. But that also might mean she is able to better articulate what she wants (DS asked for homeschooling early on, too, but since he didn't know such a thing existed at the time, his request sounded different).
DD's teacher says that the other kids in class like DD, and I know DD says she likes the kids in her class. Just not playing with them much of the time. (She *does* play with other kids at school, several times a week, but not daily.) It doesn't seem like it bothers her, but a friend would at least provide a compelling reason to go to school each day.
DS has some sensory and social skills issues that DD does not have; this contributed to some of his problems in school (and he might have been bullied by other kids because of these problems, further complicating things). DD is messy and a bit unorganized, but otherwise doesn't seem to have any LDs. Both kids are independent thinkers, strong willed, and autodidacts. There is possibly something else going on, but I can't tease it out.