Passing arguments to require (when loading module)

Based on your comments in this answer, I do what you're trying to do like this:

module.exports = function (app, db) {
    var module = {};

    module.auth = function (req, res) {
        // This will be available 'outside'.
        // Authy stuff that can be used outside...
    };

    // Other stuff...
    module.pickle = function(cucumber, herbs, vinegar) {
        // This will be available 'outside'.
        // Pickling stuff...
    };

    function jarThemPickles(pickle, jar) {
        // This will be NOT available 'outside'.
        // Pickling stuff...

        return pickleJar;
    };

    return module;
};

I structure pretty much all my modules like that. Seems to work well for me.

Yes. In your login module, just export a single function that takes the db as its argument. For example:

module.exports = function(db) {
  ...
};

I'm not sure if this will still be useful to people, but with ES6 I have a way to do it that I find clean and useful.

class MyClass { 
  constructor ( arg1, arg2, arg3 )
  myFunction1 () {...}
  myFunction2 () {...}
  myFunction3 () {...}
}

module.exports = ( arg1, arg2, arg3 ) => { return new MyClass( arg1,arg2,arg3 ) }

And then you get your expected behaviour.

var MyClass = require('/MyClass.js')( arg1, arg2, arg3 )