FDP
Welcome to A2K!
There has been an epidemic of people planning to move to Sydney lately!
Moorebank is near Liverpool, which is on the main south western railway line. Holsworthy, also near Moorebank, is on the Macarthur - East Hills line. I can't imagine any easy commute from the beach that is via rail, though. Have a look at
whereis.com.au to get an idea of your locations. Then look at
www.131500.info to get an idea of the commute.
More realistic would be somewhere in Sutherland shire, such as Engadine, Heathcote, Barden Ridge, Menai, etc., which are closer to the beach, and not too long a trip, but there is no public transport (that I'm aware of), so you'd have to drive, along the Healthcote Road. I've searched for buses along that route, without success, but there may be one I haven't found.
Suburbs closer would include Moorebank, Holsworthy, Wattle Grove. There may be a local bus service for this area.
All these suburbs could be considered family-friendly.
Good luck.