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.
To me the easiest solution would be to create a JavaScript function that could be called by your iNomads Host process to parse the iFrame data and return the information directly to the application where, if desired, you could populate the fields on the screen.
For example you could create a Javascript function and call it GetIframeData(). That function could be designed to return the data from iFrame as a JSON string.
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.
Now if the Third party API does not require any true user input I personally would simply issue a *plus/web/request on the server and process the response from that to fill in the iNomads fields. That avoids the iFrame and Javascript completely.
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.