I'd go to the more casual places - and fish n' chips on the beach or in the park is nice.
Places like Mango Jam, the Surf Life-Saving restaurant, (and the kids can play on the beach or on the grass within view while you're finishing your coffee!) The Workers club is nice as the sun sets - and there are a few casual places in the main street - a mock outback place and Rattle and Hum.
Hogs Breath was always a hit for my kids, but there is the inlet, surf club, there are a number of places and your accomadation (if you are staying at one of the may hotels in Port Douglas) can give you a full list. Mischief, well you are a bit rude aren't you, I do believe they were asking to avoid your type of people. I pitty your childhood. I guess you were never allowed to have fun. Were you made to be seen and not heard? I would love to drop my kids off to you for an hour and see if you are able to control them any better than what I can. Most parents are quite aware of what each of their children are like (OMG they are all different, each and everyone of them) and usually will find child friendly places. I Was born and Bred to the area and remember when they built the Sheraton back in the 80's. A lot has changes since then, including the snobbiness of some people. Pull your head outa ya bum Chum.
VS I hope I am never at a restaurant that you are at. Control your noisy brats and have some consideration for other diners that are paying big money to not have to put up with kids running amuck.
On the Inlet for sure. Even has the massive grouper fish they feed as entertainment. It's like a dinosaur!
I've since changed my mind about Lagoons (it's quite expensive), I like On The Inlet which really look after kids (they make sure kids food is brought out very fast), also Bucci for Italian. And also down at the Marina the kids liked Hogs Breath Cafe.
From personal experience, the Lagoons restaurant at the Sheraton Mirage is a fantastic place for kids, your kids can be noisy as there will be other kids equally as noisy! And it's a buffet which means you can be in and out fast if needed.