Will the 40mm pancake or 50mm 1.8 be noticeably better for indoor/low light than 18-135 STM?

Hey everyone - first of all, if this is better suited for the Canon Rebel forum, let me know and I'll post it there.

I just picked up the T4i/650D with the 18-135 f/3.5. One aspect of the setup that I feel is lacking is  that my indoor pictures at a modest ISO (I don't like to go above 1600) are requiring a pretty low shutter speed, even when at f/3.5. I currently can rarely get faster than 1/8th of a second, and if the subject is moving at all, it comes out blurry. Since I got this camera for use with kids/pets indoors, I'm wondering if a prime lens will help me get enough light to use a more suitable shutter speed for things that don't always sit still!

I've been really attracted to the thrifty fifty and the 40mm pancake because the price is significantly more justifiable than even the 50mm f/1.4 and 35mm f/2. I realize that the latter two lenses (and many others) would be a lot better but if I can get something good enough for $100 or $150 then I'm happy.

I've read a lot of comparisons between the 50mm f/1.8 and the 40mm 2.8 and am leaning toward the 40mm for the build quality, STM feature, and shorter focal length. However, is 2.8 enough of a significant difference from the 3.5 that I will be able to have a useable hand-held shutter speed without flash (e.g., 1/30 or better)?  What about the 50? Will it be significantly better in low light than the 18-135 or 40? I realize that the theoretical answer to both is yes, but I am wondering if there will be a practical/noticeable difference and not just one or two clicks of the wheel.

I appreciate the advice/thoughts/comments for this question and others I have asked in the past. I have learned a ton from this forum and I really appreciate your time!

-acm