Of these two sentences:

1. Die Kinder brauchen heute in die Schule nicht zu gehen.
2. Die kinder brauchen heute nicht in die Schule zu gehen.

Which one is correct and why? I'm assuming number one, since the object should be contained in the brauchen... nicht zu + infinitiv, right? Apparently the website I was doing the exercises on and my austrian girlfriend have different opinions... Thank you!