While you could emulate the inputs in iNomads its not simple as there are lots of hooks in place to attempt to Emulate the events that would occur on Windows while the user is entering the data.
Now in your iNomads panel create button and add standard PxPlus logic so that when the button is pressed you issue:
JsonData$ = %iNomads'JS_Eval$("GetIframeData();")
This will Evaluate and return the value from GetIframeData on the workstation, effectively giving you access to the data you pulled from the iFrame.
Once you have the JsonData$ you can parse it and load/update and fields you want on your iNomads screen.
Most third party website have API's that don't require true user interaction other than perhaps initial connection to obtain security clearance such as oAuth2.