Make sure it's a DSLR that she wants. If she just switches the thing to "auto" and points and shoots, she'll probably get worse photos than if she shoots with a decent mirrorless camera (Nikon J3 for example) or a good point-and-shoot. If she's interested in using the camera to its fullest potential (learning the exposure triangle -- something any DSLR owner needs to know or else they will get frustrated at certain points), and if she's interested in shooting RAW (another thing she'll learn to have to edit), then maybe look at a closer to all-in-one package.
If she's shooting at night, a DSLR definitely is the better solution. But if it's mostly day-time stuff, take a look at something like the Nikon J3 (it's on sale in Canada for $300 at Best Buy, not sure about the US). It takes lenses like any other DSLR would, but has its own lens mount system. It's more of a point-and-click kind of thing that doesn't require much knowledge.
If you want to go with a DSLR, the D3200 is, as mentioned, a great one to look at. I'd say it has the best bang-for-the-buck in terms of the sensor you get out of it (over 24 megapixels, and it's really good with high ISO, colors, etc).
So you know, the "kit lens" that comes with cameras is usually not that great (with a D3200 it would be the 18-50mm f3.5-f5.6 lens, or something like that). If you can somehow get a place to bundle the things together, and it fits within your budget, try to go for something like the 18-105mm bundled with the D3200. As far as other lenses go (I know I'm talking ahead of what your mother-in-law might want to do), keep in mind that a fast lens is going to allow her to create those really nice professional-looking photos (the kind where the background is all blurry and nice, and just the subject is in focus). Kit lenses don't do that. The reason why I'm mentioning all this is because that's what a DSLR purchase is for: quality photos, and being able to use a variety of lenses. So I want to get that information across clearly.
Here's what I would highly recommend if your mother-in-law wants something relatively compact, still high quality, and still wants to be able to use lenses but wants more of those automatic features (I wouldn't recommend it if she wants to go around shooting knowing the exposure triangle, that would be a full-on DSLR's job):
http://www.bestbuy.com/site/1-j3-compact-system-camera-with-10-100mm-vr-lens/7805053.p?id=1218860885216&skuId=7805053&st=nikon%201%20j3&cp=1&lp=3