From what I've seen, it's surprisingly difficult to get people to fill out surveys for your doctoral research...
But I agree with HK, I would suggest to OP that a little snippet on the degree-granting institution, and maybe your PI/advisor, would help parents feel more comfortable with participating, since I presume you are asking for some personal information here.
You might also try directly contacting institutions like Davidson's, Duke, JHU, Robinson Center @ University of Washington, etc. and asking if they would allow you to send survey packets/links for them to forward to their student lists.
