Canon and Nikon don’t really make a bad DSLR. They make great ones, fantastic ones, and then “holy crap I wish I could afford this” ones. As cameras get more expensive they have features and qualities that let you work more quickly and make getting your shot a little less frustrating. But if you know what you are doing, you can take professional quality photos with any of them. T5i included.
As for moving subjects in low light, you have two choices.
First you can get a fast lens with a wide aperture. Something that goes under f/2. The Canon 50mm f/1.8 is only a hundred dollars. That will get you part of the way there. The next step is finding an ISO value that will get your shutter speed fast enough to capture moving subjects. If your subjects are moving somewhat slowly, you can shoot for around 1/100th of a second. If they are running or playing, you will have to try to get around 1/200th or higher. (These are ballpark shutter speeds. You may have to adjust a bit depending on the situation.)
Once you have your fast lens affixed, set your aperture to it’s lowest f stop. Half press the shutter button and meter your scene. Look at your shutter speed. If it is too slow, keep raising your ISO until you hit your 1/100 or 1/200 target. In some cases you may have to go to an ISO of 3200 or 6400. This will introduce a lot of noise into your image. It’s the price you pay for being able to stop motion in low light. If it is pitch black and there is absolutely no light… tell them kids to stay still. There is not a magic see-in-the-dark-at-fast-shutter-speeds camera yet.
The second solution is to use flash. This may not be a great solution for outdoors, but if you are inside in low light, you can make it work pretty well. I usually recommend people not use the pop up flash. If you take a lot of these types of pictures, I highly recommend saving up for an external flash with a swivel head. Something with TTL or ETTL metering. You can get the more expensive Canon name brand flashes, as they are all excellent, but I have been really impressed with my Yongnuo flash. The build quality and reliability aren’t top notch like the Canons, but they work great for most folks and are quite the bargain.
Once you have a flash, remember never to point it straight on unless you absolutely have to. Angle the head towards the wall or ceiling. Preferably a white-ish surface if possible. This will give you smooth, even lighting and vivid pictures. If things start moving fast, just lock your shutter speed to 1/200th (or whatever your flash’s max sync speed is) and start shooting. Set your ISO nice and low and you won’t have any worries about noise.