b) <h:commandButton value="Login"
both are enclosed in h:form.
Issue is whenever there are two browser instance rendering the same page at same time, neither the valuechangelistener of radio button nor command button working. if i close both browser and access this page in new browser, both of them are working fine.
Any pointer to issue and solution is highly apprecitaed.
I'm afraid that I can't tell anything by looking at your samples. They are hard to read, but seem to be basically correct. Although I'm not sure that you realize that the valueChangeListener doesn't fire until the "Login" button is clicked. Listeners do not fire AJAX events. Or any other kind of asynchronous event. In fact, they don't fire events, period - they listen to events.
An IDE is no substitute for an Intelligent Developer.