How are you going to see the photographs that you will be shooting? Any printing beyond 8x10?
RX100 has a fast autofocus and very good movies but zoom is limited.
If you don't print large or you only see the images on a monitor the Sony HX30V (or maybe it's succesor) is very good: very fast focus for a compact, including at the long end and with poor light, easy to use, very good movies, starts wider and has a much longer zoom; just don't enlarge the photos beyond 40-50% (has 18 MP to start with).
It prints just fine up to 8x10, maybe bigger with the right image and settings (I have a good print of 11x15 or so for example). If you don't need additional controls, including raw, and you don't print large the RX100 doesn't offer anything beyond the HX30V (particularly as a family P&S) and I have both; it also offers WiFi which is actually working this days, even if it remains clumsy.