Not sure if this answers you.
I had a similar request to create a URL on an existing report to download open/render a report directly in pdf. My report had a parameter of year which had to come from the parent report.
Both the parent and sub report were deployed to the same folder
I used this as an action on the text/texbox - go to URL and set this as the URL expressions:
="http://ohtwi1sql002/ReportServer_BGCO/Pages/ReportViewer.aspx?%2fDEV+AND+QA%2fDirector+Scorecard%2fBGCO+Summary+pdf_print&rs:Format=PDF&year=" + Parameters!year.Value