Best DSLR + lens combo for low light, indoor kid shots

The situation you're facing is the most difficult one possible: Low light + fast subject movement + close camera-to-subject distances.These conspire to make huge demands on the camera/lens system:

• Fast subject movement forces high shutter speed.

• High shutter speed combined with low light forces large aperture, even with high ISO.
  

• Large aperture combined with close camera-to-subject distance results in very shallow depth of field.

• Shallow depth of field demands extreme accuracy in focusing.

Thus, you need equipment which can track focus with extreme accuracy on rapidly-moving subjects in low light. Top-end professional dSLRs and lenses have autofocus systems which can do this, but I'm not aware of any inexpensive gear which can.