What do you mean?
It is a camera with interchangeable lenses, in layman's terms a bit like a smaller version of an SLR, and not really suited to your needs at all.
I have an SLR and a compact, if I could only have one camera I'd have a compact (and until recently that was the case) as it is always there ready to get a shot. Out of pocket, point, click, done! Exactly what you need to capture those times that you are enjoying with the family.
As for recommending one... The Canon Ixsus range seems to do a good job, I'm also pleased with my Nikon Coolpix S4300 but that was at less than half your budget due as I don't treat my compacts well (Mountain bike, beach, thrown in the bottom of bags etc.) so probably wouldn't be of use as a direct recommendation.
What I would recommend is getting yourself down to your local Jessops or wherever has cameras on display ready to go and actually give them a try. The picture quality of most cameras is very good these days (just stick with a decent brand) and the bigger difference IMO is in the feel and usability of various models. I would personally start with Canon and Nikon then see how you go from there.