In low light situations, fast lens are better. The best Canon zoom lens would be the EF-S 17-55 f/2.8, but that lens is way out of your budget. The Sigma 17-70mm f/2.8-4 lens would be in your budget. I have no experience with this lens. I have seen reports of people very happy with it, but I have seen a few reports of people having focus problems with it, like many Sigma lens on Canon cameras.
A prime lens like the EF 35mm f/2 also fits in your budget and would be a good choice.
I know you asked about lenses, but for indoor shooting you also need to learn how to use high ISO, even with fast lenses. You do not want to use your fast lens wide open all the time because of depth of field. If you take a picture of a group of 5 or 6 family members standing around at f/2, they are not all going to be in focus. You sometimes need to stop the camera down to get the depth of field you need. You can use flash or very high ISO. Flash is ok, if you learn how to do bounce flash. I think direct flash pictures don't look very natural.
The other choice is very high ISO. I've taken a lot of pictures indoors at ISO 6400 on my 60D. Raw these pictures look very grainy, but after putting them through noise reduction in Lightroom 3, they come our amazing good looking. Clearly they have lost fine detail compared to an ISO 100 picture. You would not want to make 24x36 enlargements from these pictures, but cropped some and reduced to a size you might display on the web, they look very good.
I have made some comparisons with the noise reduction in the free Canon DPP software. Lightroom 3 seems much better to me. I also compared Lightroom 3 NR to NIK Dfine 2.0 and I could not see much difference in the results, although the Dfine 2.0 package seemed to give you more control options. I have heard that DxO Optics Pro also has very good NR and there may be several more out there. This kind of software is not cheap or real easy to learn to use, but it does add another tool you can use with any lens in a low light situation.
The thing to keep in mind is even if you are using your f/2 lens at f/5.6 to get the DOF you need, your auto focus system operates wide open. That is the big advantage of a fast lens in a low light situation. It will AF better in marginal situations.