I see two possibilities (there could be more):
- Your son really does have ASD, and he has a sufficiently high IQ that he is self-treating in a manner similar to ABA by examining what is normal and trying to replicate it himself and with those associated with him as family; OR
- Your son does not have ASD but rather some other sort of social anxiety disorder that causes him to get stressed out in social situations and when he perceives his sister doing things that will cause your family to be perceived as social outcasts.
In both cases, it is noteworthy that there was no one there to witness the behavior other than family.
In either case, perhaps your son has reasoned logically that if he allows his sister to act atypically amongst family, then she may begin to do it elsewhere too such as in front of his peers. It is reasonable to nip this in the bud from his perspective.
Alternatively, if he is self-treating his ASD, then his sister's departure from what he perceives to be "normal" maybe frustrating. It may be that he does not understand why she is behaving this way, and he does not yet understand the concept of "normal in context." He has observed that it is not usual/normal for people to sing and dance in public places (other than dance halls, clubs, etc.). Her doing this in the car is perceived as abnormal, yet you didn't take issue with it. She is skewing his observations of what is normal, which takes painstaking effort on his part. It is frustrating because her behavior sends him "back to the drawing board," and it is easier to simply single her out as an isolated, abnormal person. If he can get her to conform to his existing perception of normal, then he does not have to change his own carefully crafted "normal" behaviors. What he lacks, if this is the case, is an understanding that what is "normal" can change or shift in various situations, contexts, and settings. Being alone with family, it is normal for one to feel freer to self-express by singing or dancing than in, say, the middle of a funeral in public. I think this is more likely than another form of social anxiety, given that the incident occurred amongst family.
However, my older sister used to try and coach her younger siblings on how not to embarrass her in public, especially around her friends. She is not on the spectrum (adopted, so my genetics are not a factor). I have long suspected she is a histrionic - always needing attention and willing to go to extreme to get it. Conversely, anything she thought my cost her that attention, she fought tooth and nail...