There is also Flanagans at Rathdowney which seems to be very popluar with families too. http://www.flanaganreserve.com.au
And like Bigriggin it also gets busy at peak times....you would need to book either of these places in advance.
I know Troy does not think Island Reach or Kennilworth Homestead is suitable but they are both very popular with young families. I have friends who have 3 young children and they go often to Kennilworth Homestead and think it just great and in the many times I have camped at Island Reach there have been many young children there also. You can camp well back from the water if you feel you may have a problem.
You have quite a lot to choose from given the requirements that you have listed. I would suggest that you check out the websites and ring the various places and talk to the managers and see how you feel about what they have to say.
Some you may like, others you may not and then you may feel better informed to make a decision.