The IS will help eliminate blur from camera shake, but this lens is slow, so you would have to use it with a flash to get decent indoor candids of children playing. The IS does not help eliminate blur from your subject moving at slow shutterspeeds, it's only to help eliminate blur due to the photographer not being able to keep the camera steady. For me, 75mm is too long for taking candids of my kids "around the house" ... if you have a tight budget the Tamron 28-75 (or Sigma) is fast and would work well for indoor candids. I have the Canon 24-70 f2.8L which has been superb, but it is a bit expensive and some don't like the weight (not an issue for me).
Also, if you can possibly afford it, the Canon 70-300mm f/4.5-5.6 DO IS has better image quality than the 75-300, and is about the same weight but an inch and a half shorter. Still a bit long to me for an all around lens for taking indoor candids and again is too slow to use indoors without a flash.
I hope this helps.
Bob