I'm just an amateur but I like photography and taking as good a picture as I'm capable of. I don't mind carrying extra equipment and understand something about photography (what aperture is, what different shutter speeds do etc.) but I'm no professional.
Last year at this time I replaced my Sony F717 with an FZ30 (8 mp camera). While others could take nice pictures with this camera, I couldn't get anything out of it thatI thought was better than the F717 (and rarely as good as that 3 year old camera), so sold it after a month and got a 6 mp dSLR.
Some of the newer advanced p&s cameras (Sony's H5 comes to mind)are taking good pictures that appear to be better than what I got out of the FZ30, but I still think the budget dSLRs are better. They all have auto settings, so you can use them as an automatic camera (I've handed my Pentax DS to my husband who's never owned a camera in his life and he's taken some really nice pictures with it). However, there is a certain learning curve to using them if you don't have a photography (film SLR) background and want to get something specific from the camera.
What is acceptable quality depends on the eye of the beholder - the person who bought my FZ30 was perfectly happy with it. They had no interest in all the extra equipment or knowing what aperture is or does. I, on the other hand, had owned a Pentax SLR in the 1980s and was too sentimental to get rid of my equipment when I bought the Sony, so now I'm using nicelenses I bought in 1980.
Any of the budget dSLRs will take excellent pictures. Since you want to take action pictures in low light, try to buy fast lenses (smaller aperture numbers, like something between 1.4 - 2.8). I have the Pentax K100D and love it (image stabilization in-camera so any lens is stabilized), but any of the budget dSLRs take great pictures.
P.S. If I were in your shoes, I'd probably choose the K100D (6 mp)over the newK10D (10 mp). The K100 might be "only" 6 mp, but if you are only going to take family pictures and print up to 8x10, the extra MP of the K10 won't matter. The K10 is a brand new camera and you'll pay full price, while the K100 has been out for several months and can be found discounted. I'd put the difference in cost into buying better lenses because they can be used on your next camera.