Yeah, I think my DD is pretty lovable in general except when she is being excessively bossy but objectively speaking, I don't think she'd be the type most teachers would see as an ideal student with a halo around her head. This could change in the next few years but she is the type who would be a decagon if someone tells her to stop being a square and be a circle so unless she gets a teacher who thinks that's actually clever and funny, she won't be coming home with the student of the quarter ribbon, not that I think that's important.
But I have been to his class once and had a chance to see how easily lost he gets in there and feels the need to talk and ask more questions because we keep telling him that he goes to school to LEARN.
K has gotten a little bit more academic since Common Cores but I think most experienced K teachers still believe K is about socialization, readiness skills, and learning to be at school. Even if you don't have a super genius at hand, I think the first 3 years (K,1, & 2) are problematic for precocious learners unless they are complete extravert who are happy as long as they are around their friends.
How would having your DS1 at home full-time affect your DS2?