Hey, I'd look to create a custom login widget, that you login into with another sites credentials and it redirects you to that website? Both sites use different credentials.
How would I go about doing this?
You can extend the bulit-in identity providers by creating your own:
After the user has logged in, you can do a client-side or server-side redirect to that website.
There might be a bit of ping-ponging between the two websites, depending on how you implement it.