I guess you need to establish a convention ...
First, there isn't really a way to construct parent/child relationship between proxies in Apigee. That relationship is your design, an artifact of how you are organizing your proxies. I suppose it means a client invokes proxy1, and you have configured proxy1 to invoke proxy2. In this case proxy1 is the "parent" and proxy2 is the "child". That's your design, and that's fine, but there's nothing in Apigee that explicitly supports this idea of parent/child dependency.
By "convention" I mean the establish a way to transform and pass query params and payloads from the "parent" to the "child". One possibility: parent receives query params a, b, and c with various values. The parent maps a to parent_a, b to parent_b, and c to parent_c, then invokes "child".
Child receives query params parent_a, parent_b, parent_c.
For the payload, ... if the parent is also passing a payload to the child, in addition to and distinct from the payload that the parent received from the original client, then you'd have to have a way to encode the original payload and attach it. One possibility is to encode it with base64 and then attach the encoded value in an HTTP header.
But what is the purpose of this?
What are you really trying to accomplish?
What are we solving for?
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