lighting - How can I take natural looking photos of my kids, etc. with a compact camera indoors?

I have a Panasonic lumix fz47 and when taking photos inside, unless I have a lot of window light, the photos are always a slightly funny colour or a bit grainy. When I use the flash it is way too bright and the photos look awful.

How can I take natural looking photos of my kids inside? What settings should I use?