When I got into photography in a serious way, my photography instructor drove home the idea that slow lenses were for amateurs and fast lenses were for pros. Part of the reason for this was cost. Fast lenses cost a lot more money. An f/3.5 lens was a lot less money, and also weighed a lot less, than an f/1.8 lens.
The above shot of my wife blowing out the candles on her birthday cake, surrounded by her grandchildren, was shot available. I had the lights turned out in the dining room but there was some light spilling into the shot from a distant kitchen.
I made sure the three were facing the lit kitchen and not the dark wall behind them. The positioning was under my control. I see nothing wrong with taking a little control when shooting family pictures.
The shot may be a little grainy but I can live with that. I like it much more than a shot done with an on-camera flash that provides a cold blast of light illuminating the scene in an unattractive, flat, shadowless manner. (And a faster lens helps to keep the need for ridiculously high, image-damaging fast ISO-speeds, to a minimum.)
If I were buying a point and shoot today, I would make sure it had a least an f/2.0 lens like my now aging Canon S90. Do a google search and you will find there are even faster point and shoots out there today.
Remember, the smaller the f/stop number the faster the lens. f/1.4 is a full stop faster than f/2.0 and two full stops faster than f/2.8. And even with a fast lens, try and brace the camera while taking your shots. A steady camera is important even with all the image stabilizing technology used in making cameras today.
And as most point and shoots suffer from camera lag, I find shooting bursts of shots and just not single pictures helps to capture the moment. With some cameras this may force you to accept smaller files but this is not a problem if you are not making enlargements bigger than eight by ten.