Yeah, I think the problem (if you permit me to label it so) is often less with recognising emotions, and more with diagnosing why someone has that emotion.
In the given example, it may be apparent to the child that mum is angry/annoyed. But they are likely to be confused as to why.
(which is where DoreenMichele's point about educating the parents comes in - if they can clearly articulate how they feel and why in a given situation, then the autistic child is likely to be able to learn and remember this, even if it might take them a few repetitions of the situation for it sink it (like anyone learning anything that isn't intuitive to them))
In the given example, it may be apparent to the child that mum is angry/annoyed. But they are likely to be confused as to why.
(which is where DoreenMichele's point about educating the parents comes in - if they can clearly articulate how they feel and why in a given situation, then the autistic child is likely to be able to learn and remember this, even if it might take them a few repetitions of the situation for it sink it (like anyone learning anything that isn't intuitive to them))