As everyone said, a DSLR is a matter of personal taste. I LOVE my Canon, even though it is the smallest, 1000D (Rebel XS?). I hope to update next year to either the 550D or 60D.
But I would also like to point out another option to you. From what you told us, I gather a DSLR will be a BIG investment for you and you will likely want a decent zoom lens. Problem with those is: A bigger zoom range comes by the cost of lower light sensitivity. Unless you pay a LOT of money! So for someone shooting fast kids, indoors and who isn't used to the weight of a DSLR, you might want an image stabilised lens. These things are pricey. Then add a good bag (and with a zoom attached you can't go too small), extra batteries, memory cards, tripod ect. It's not a cheap hobby. Especially considering you plan to shoot in Auto for a good bit that might not be worth it.
So to me it sounds like you're a good candidate for what in Germany we call a "bridge camera". Those look like really small DSLRs, but you cannot change the lens. So it's in the middle between a p&s and a DSLR. They come with bigger sensors than a p&s, better/bigger lenses, a good zoom range, build in stabilisation and usually you can turn them to manual mode, too. They do not offer all the freedom of a DSLR system, but I think they will get you very decent photos for a cheaper price. And it might be a good option to take some steps into manual, without the guilt having spent tons of moneys on features you rarely use.
Don't get me wrong, a DSLR with a good lens will give you superior image quality in Auto, too. But if you don't spend a good bit of time learning manual I think the difference won't be as big as to justify the money, IMO. And a lot of people buy a DSLR and then don't want to drag the heavy thing around all the time. And a normal body with a bigger zoom IS heavy.
For example this is a Canon "bridge camera", the PowerShot SX20 IS.
http://www.amazon.de/Canon-PowerShot.../dp/B002LISH1I (sorry it's in German)
As you can see it has a lot of features a normal p&s hasn't, the same range of auto and manual settings as the DSLR and you can even attach an external flash. I believe there is a 30XS out now, but you'll get the picture.