You can do something like this in your parent form:
var url = "/Sites/YourSite/Lists/YourList/NewForm.aspx?CustomKey1=First value&CustomKey2=Second value
spjs.dffs.redirect(url,false);
Then, in the child form add this in your Custom JS:
setFieldValue("Your_target_field_1", GetUrlKeyValue("CustomKey1"));
setFieldValue("Your_target_field_2", GetUrlKeyValue("CustomKey2"));
Replace Your_target_field_1 and Your_target_field_2 with the internal name of the fields.
Alexander