I am using Webpack with firebase and firebase-admin.
To install firebase I ran
npm install --save firebase
I am importing firebase
I know you've sorted your problem but there's no real answer to the original problem.
The problem wasn't with the node_modules, it was with the way that you were importing the component.
When you export a component ES6 way you normally do export default () => { console.log('default component export'); };
default is the keyword here, when you import a component ES6 way like import firebase from 'firebase' it's grabbing the default property from the exported object.
Keeping in mind the above example, here's what you've done wrong.
Using ES6:
import * as firebase from 'firebase'
console.log(firebase.auth) // Undefined
console.log(firebase.default.auth) // Function
Using ES5:
var firebase = require('firebase')
console.log(firebase.auth) // Undefined
console.log(firebase.default.auth) // Function
Note the .default
Hope this helps to explain what was wrong in the first place.