Chrome has a lots of comand line switches for things like window-position etc.
If you just add the url to open to the command it should open that page for you.
You can test all these outside of Node-RED then move them to the exec node when you have it working.
Have you thought of using the WDIO nodes? They are geared towards web automation (think of Selenium on steroids). They definitely let you open a browser, connect to specific URLs and input / read data from the browser. You can also resize the browser to specific sizes. I'm not sure about the 'position on different screens' aspect though.
WDIO offers an enourmous set of capabilities - possibly more than you need.
Note: if you go this route I'd recommend 'selenium-standalone' (npm package) be installed on the machine you want the browser to be executed on. This also means you need to have basic Java and run it from a shell session.