The Canon S95 ticks all your boxes except for the swiveling LCD. I believe there are only two compact cameras in the market that have a swiveling LCD: the Canon G12, which is more than $400; and the Samsung TL500, which does not offer HD video.
We are looking for a new digital camera - we currently have the Canon Powershot A80 (quite old!). We will be taking shots of kids, indoors and out. We want good quality pictures, good low light pictures and HD video capability. It would be nice for the LCD to swivel. Have been looking at Canon and Nikon, but we are open to others. We don't want to spend more than $400. Getting very confused with all the options!