|A word of warning from Alnwick Castle|
Whilst treading a little bit carefully in this area, I find the Woodman paper to be intriguing. Not only because their findings provide further support for the fluidity of presentation in autism tied into the concept of stability (see here), but also because of that association between presentation and environment .
A quick trawl through the peer-reviewed literature on this topic reveals that family context is something previously covered by this authorship group as per other papers . Some of their other discussions  looking at the role of families on autism carry some pearls of wisdom, as for example: "It is important to note that within any family system, transactions among family members are bidirectional. As such, in addition to risks for parental health due to stressful caregiving, high levels of family distress also can create difficulties for the individual with autism". That last paper also talked about the use of a "multi-family group psychoeducation" intervention model (see here) as a means to improve the family dynamic which is something I'd like to see quite a bit more research into.
Music to close, and what else but Praise You by Fatboy Slim...
 Woodman AC. et al. Change in Autism Symptoms and Maladaptive Behaviors in Adolescence and Adulthood: The Role of Positive Family Processes. J Autism Dev Disord. 2014 Jul 29.
 Smith LE. et al. Symptoms and behavior problems of adolescents and adults with autism: effects of mother-child relationship quality, warmth, and praise. Am J Ment Retard. 2008 Sep;113(5):387-402.
 Smith LE. et al. The family context of autism spectrum disorders: influence on the behavioral phenotype and quality of life. Child Adolesc Psychiatr Clin N Am. 2014 Jan;23(1):143-55.
 Smith LE. et al. Adults with autism: outcomes, family effects, and the multi-family group psychoeducation model. Curr Psychiatry Rep. 2012 Dec;14(6):732-8.
Woodman AC, Smith LE, Greenberg JS, & Mailick MR (2014). Change in Autism Symptoms and Maladaptive Behaviors in Adolescence and Adulthood: The Role of Positive Family Processes. Journal of autism and developmental disorders PMID: 25070471