D-SLR certainly helps to get better indoor and low light action photos, but usually not at the price $1000 or below. Usually will need a 70-200 mm f/2.8 zoom lens or a prime lens with f/2.8 or larger aperture (smaller f/number). This kind of fast or bright lens will cost $1000 or more by itself.
However if you really need to stay around $1000, then you can try Canon XS with 18-55mm IS kit lens selling for about $550, and buy the Canon EF 100mm f/2.0 which cost about $450. You will need the 100mm f/2 for indoor sports. The 100mm will have 160mm reach on this camera. This is not much zoom, so you will likely need to do some cropping. But f/2 aperture should get you some nice and sharp photos, though you have to learn how focus with a large aperture lens.
If my budget is $1,000 and I want a DSLR plus a second lense (zoom) what should I buy? I most like to shoot my kids' baseball, football and wrestling and basketball. I have a Canon Powershot XS 100 8mp 10x optical now. I take lots of picture because I crank out the team slide show. I want more, good action shots. I can't take good photos for wrestling and basketball now because indoors and poor lighting. Will DSLR help with these sports? Thank you! Evfab4