thanks for the kind offer re child seat! We are ok at present - hoping the govt works their crap out soon!
airport train - one way is $14.60 per adult, $9.90 per child, return is $22.20 and $15.20 resp. Yes - a major rip off...taxi should be around $40 - maybe less as you are way outside peak period but some of that is tolls - eastern distributor - another white elephant, another story - oyu can ask your taxi driver to avoid this road - at 6 am (or 5.30!) - should significantly decrease cost of trip even though you have to drive a bit further to go around...
as you have discovered - sydney admission prices hurt a bit (lot) - some musuems have free days - powerhouse i think is first sunday of month...not sure if that fits your dates but worth exploring at eacj place you want to go...we can but apologise!

just founf another site for you to check out
http://www.seesydneycard.com/index.html
its a deal card for sverela attarctions etc...may be worth looking at if you are really organised and plan to squeeze things in to a couple of days

also look at
http://www.visitnsw.com/Sydney_for_Kids_p685.aspx

i will keep checking this thread...