Web automation in python?

I'm finishing off learning python and wondered how I could go about doing the following. I have seen this done in js and jquery, but that's not my area. I am trying to create a web page where my user can log in and interact with site b through my site (site a). Eg a user enters their login details for site b into site a; site a sends them to site b, and site a acts upon the response of site b. Eg if login = success: run loginsuccess /// loginsuccess would be able to grab data from site b and display it on site a (basically the user is able to interact with site b via site a)/// else: print 'fail'

I've seen web automation in python, but not like this, it mainly sends me to site b; or is browser only. I know this is possible in other languages and I know this has been bought up before. I'm asking is this possible to create as a script written in python and put it on my server?