Welcome to the forum!
I would definitely chose the Canon Rebel, of the two, though for an active toddler, a lens upgrade would be a good idea, something like a 28mm or 35mm non-zooming, fixed-focal-length "prime" lens. Of course, an infant will take a bit of time to become a toddler, allowing time to save for the "faster" lens. If affordable, the new 24mm, 28mm, and 35mm Canon lenses, with 2.8 apertures and Image Stabilization, are examples of "faster" lenses aimed at the video-shooting users, who want Image Stabilization.
My first digital SLR camera was a Canon Digital Rebel XTi, a distant ancestor of the T-series you are considering. It was, and still is, capable of capturing images of fast-moving children and dogs, though it preceded the era of video-capable digital SLR cameras, so I cannot offer advice on video. (I remain uninterested in video, in spite of owning a pair of quite video-capable Canon 7D cameras today.)
Any decent tripod will work with the Canon; tripods and mounts intended for modern cameras are, normally, universal.
While I have only partially addressed your questions, I hope I have typed something useful, and this reply will "bump" your topic upward a bit.
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