Some airline lounges have "family rooms" which are separate from the main lounge area and are often separated by a door to keep the noise level in the main part of the lounge down. I realize you paid a premium fare to fly business class but that doesn't entitle you to disturb others in the lounge with the noise of your rambunctious two year old. Others who also paid a premium for their tickets or who pay annually for lounge access have the right to enjoy a quiet atmosphere. I'm not sure why you were so offended by the lounge staff asking you to quiet him down. It's their job and since, as you say, the noise went on for an hour before they approached you they were probably doing so because of a complaint from someone else in the lounge.
As for your impression of Austrian Airlines being "kid friendly" here is the information, in English, from their website on traveling with children:
All of this information pertains to services for children in-flight. There is no mention of any special amenities for children in the lounge.