I'd also like to comment and share what I've learned.
Firstly, I never use the "auto", "P", "S" or "A" settings anymore. They were easy to use when I was new with my Minolta A1, but I CONSTANTLY got either blurry or underexposed pics. Talked to a friend who gave me some "settings" to use on manual mode. Tried it and never looked back.
I also have kids and I like taking shots of them doing things at home. Lighting at home is very "HDB" and so I also face similar problems with you. My Minolta doesn't handle ISO400+ well at all. (But like one post earlier mentioned, depends whether you like to view at 19" full screen).
The settings I've used on mine are typically zoomed at about approx 180mm, ISO 200, f/3.5, and shutter 1/125 with flash on. My shots of the kiddies at shutter speed less than this turn out a blur photo - kids can't keep still (and candids are my favourite of the boys).
Hence, yes, as much as I hate using a flash, I don't have a choice. So I use the external flash, point it up to the ceiling, bang - light up the room (so it doesn't seem like only 1 subject is lit with the background dark) and voila! The snaps turn out pretty alright.
I hope this helps to bring up your confidence. My lesson learned is don't trust those "auto" settings. Trial and error with manual mode and find out what works on your cam. From one newbie to another newbie - keep trying!