Great Place to take children
Being born and bred in Melbourne i can assure you that Melbourne Park is extremely child friendly and very easy to access from CBD Hotels.
The Open venue has a great grass relaxation area with ample shade if you choose to attend daytime sessions and at night they have many activities including a giant screen showing the main arena matches.
Being that the Open dates are during our school break, there is no shortage of teenage babysitters looking for work so should you need to have your 2yo sat then there wont be a problem.
If you want any advice at all on accomodation/restaurants etc. l will be only to happy to offer you local recommendations.
Enjoy your trip.