anxiety at school and meltdowns at home

I have recently become a SENCo at a large comprehensive school.  A number of pupils that I have with ASD are showing the 'Jekyll and Hyde' characteristics (Attwood).  In other words, they are behaving well and fitting in at school, but having huge meltdowns as soon as they get home.  I would love to be able to support parents, as well as these pupils.  Has anyone got any ideas of what I can do at school to help, when there don't appear to be any problems and the pupils aren't verbalising any issues?  Thanks