If your service does not have the REST DPH and/or you are not able to re-record, you will need to make manual adjustments in the VSM Listen Step (to add and configure the REST DPH) and the VSI (to support the changes the DPH will apply when it executes).
When you use the REST DPH, URLPARAM0 will map to your account number (123) and URLPARAM1 will map to your child id (345).
The REST DPH will parse the URI and create two arguments. It will also alter the Operation name when the URI and rules you have applied are executed.
The parsed arguments are passed into the VSI as URLPARAM0 and URLPARAM1.
The REST DPH will also modify the Operation in the VSI to: GET /account/{URLPARAM0}/child/{URLPARAM1}
So, for the operation, GET /account/{URLPARAM0}/child/{URLPARAM1}, you will see two arguments in addition to any query string data or body data that may have also been parsed.
One would use the specific transaction feature to compare these properties for:
URLPARAM0 = 123
URLPARAM1 = 345
to select the desired response. DevTest does it this way so that additional account IDs and Child IDs simply fall under a single operation.
Consider the VSI picture below. Notice the difference in the Operation. It no longer carries the value that came in on the REST call; rather the parameter URLPARAM0. The REST DPH did this. Also, notice that the URLPARAM0 has been copied into the Argument list. (Some information in this VSI is intentionally hidden). The tie breaker between one transaction and another is handled by the comparison operator (i.e., when the URLPARAM0 = "1111111111" and query = "newest" then send this response).
Once the REST DPH fires, you can use script logic to access the if (lisa_vse_request.getArgumentList().containsKey("URLPARAM0") ) to check if the argument was parsed.
Hope that help clarify a bit.