So unless you're willing to get a DSLR, learn to live with using your flash indoors or getting soft, noisy OOF images of your child(ren) indoors unless you flood the room with light..
Sorry- that's just the way it is..
I mostly agree with R Valentino although I also struggle to get clear pics of my kids even with my DSLR, 50mm F/1.8 lens and the ISO cranked up unless they're sitting still. I would say flash is a must indoors with moving subjects. Image stabilisation is only really any good with still subjects..
If you don't want to go down the DSLR route (I would strongly recommend that you did for your requirements) you could try one of the super zoom cameras that can take an external flash. Can the S5 IS? I'm not sure. Then get an external flash to go with it. The difference will be night and day compared to the built-in flash (excuse the poor pun!)...
The S5IS is one of the top P&S made. It is, nevertheless, drastically inferior to a DSLR in low light. That's what most of the reviewers are comparing it to..
It does have two nice features compared to other P&S. First, you can zoom while recording a movie. Second, it can take an external flash..
Unless you're considering a DSLR, the S5IS should absolutely be on the short list...
I agree with Greg on the merits of the Canon S5. I also considered the Panasonic FZ50 because of it's hot shoe, flip LCD, and larger sensor size. The FZ50 appears to have slightly better image quality. BOTH have almost no shutter lag.ngk20000..
The Fuji S6500 is not a compact P&S but has good indoor performance because of it's low light sensitivity and flash that does not washout everything at close quarters..
It also has a focus assist lamp that helps in very dark situations to help the auto-focus..
This camera is quite responsive if you dont go too far on the zoom and because it doesn't have IS this is also a good reason to keep towards the lower end (below 200mm)..
The video mode is excellent because of it's low light capability. I have used the camera very sucessfully in rooms that are very poorly lit such as dancefloors that are lit with 'romantic' lighting..