Great question! I am interested in similar research related to children with autism. A lot of research suggests parents of children with autism report higher levels of stress than parents of typically developing children and children with other developmental disabilities (including those with down syndrome). Research has also suggested a bidirectional relationship between parental well-being and child challenging behavior.

Regarding children with Down Syndrome specifically, I am less familiar with research related to bidirectional relationships.

Some related articles might be:

http://www.aaiddjournals.org/doi/abs/10.1352/0895-8017(2004)109%3C237:PWACIM%3E2.0.CO;2

http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2788.2005.00699.x/full

http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2788.2010.01258.x/full

Wish I knew more of the research related this population but I hope this might provide some initial directions!

Thank you very much for your contribution to the discussion.