Camera Help and Suggestions

What is your budget?

I would recommend going Digital SLR. You can get a similar priced package to the Nikon 1 or even go a bit higher and get even more goodies. The nice things about digital SLR is the interchangeable lenses, the lenses themselves are an investment - upgrade the camera body and you can use your previous lenses with it. It sounds like she could use the versatility of the SLR simply due to the verity of subjects she likes to shoot.
Now on to size, A DSLR will be a little bulkier than your point and shoot variety but with a camera case you can pack everything nicely and it should fit in the bottom of a backpack for hiking and camping. Different camera bodies will be heavier than other so just shop around.
DSLR offers someone the ability to shoot in different formats. One such format is called RAW; it allows you to make the most adjustment to your picture to include Brightness, Contrast and even Hue and Saturation. This is a natural adjustment not just photo correcting like with JPG image. I'm not sure point and shoot varieties can do that.
Anyway, food for thought! Good luck in finding her something.

The Nikon 1 has interchangeable lenses. These days a DSLR is not required for that, and hasn't for a long time. I happen to prefer a DSLR for a number of reasons, but size and weight are not a top priority. Many good EVIL (Electronic Viewfinder Interchangeable Lens) cameras abound. Most newer ones come with an eye-level viewfinder so it is no longer necessary (although still possible) to hold the camera at arm's length. Viewing can be done at the eye like cameras used to be, which make them much more stable to hold, and more easy to view in sunlight.
Most EVIL cameras these days have in-built stabilizers, and shoot HD video also. Features are typically similar, so is size and weight. Where differences exist are in the size of the sensor. Some are the size of a postage stamp, on up to the size of a 35mm negative or slide. The latter pushes the cost and size to the higher end, but if you're going to be doing large prints, the advantages outweigh the cons. If your end-use is digital display or the web, then top-end cameras are a waste of money.
Sony, Panasonic and Fuji are makers of the top EVIL cameras. Nikon and Canon make them, but keep them on the low-end side so as not to cannibalize sales of their bread-and-butter DSLR's.
Also you can get a lot more bang for your buck by buying secondhand. Stay away from fleabay, buy from a reputable outfit like keh.com where they have a trustable grading system and a 14-day no-hassle return followed by a lengthy warranty.

Nikon 1 v3 is a flexible camera with interchangeable lenses. Meets the weight and size requirements, quality shots for a small sensor camera. Blurring is usually a problem with the shooter either in settings selection, or camera handling. It doesn't sound as though she has outgrown the unit.
My suggestion is, she studies an unacceptable shot and determines where she or the camera settings messed up. The J1 is more than a "point and shoot", it can capture great shots when used correctly. My wife shot with one for a couple of years, colors are vibrant, auto focus quick and the lenses are all acceptable sharp or better throughout their range. Her J1 was simply great at "macro" with flowers. With photography its an understanding of the gear and how the shooter sees. Seeing and using the equipment to capture the wanted shot is much more important than the equipment being used.
A DSLR will be weighty and additional lenses add more weight and require larger bags. The only reason I know of for her to consider a change to DSLR would be for the larger sensor. The bigger lenses, bodies and etc. will most likely make for too much baggage and weight. If you do make a change, spend the money and go "full frame" as the larger pixels capture more information.
As background, I've shot professionally for many years (predominately wildlife), mostly Nikon equipment, sold photo gear and taught. I can say the Nikon "firm ware" is probably the finest available and handles data exceptionally well. I really doubt she is even close to over taxing the capabilities of her current camera.
As an aside: Capture the shot in the camera as often as possible. Sitting in front of a monitor trying to salvage a shot is wasted shooting time. I hate doing such! Getting it right in the camera is the goal. If you are always changing exposure of a file you are not thinking the shot through and getting it right. Checking settings and thinking a shot into the camera will soon become second nature.

Unless the 2011 Nikon 1 is very different from the current one it's a very capable interchangeable lens camera. The current one is around 1100 bucks with a kit zoom and will take a variety of glass, will shoot RAW, and has continuous autofocus. It's compact but it's far from a point & shoot rig. A DSLR would be an upgrade primarily in the sense that it would have an eye-level viewfinder instead of a back screen only but if okiebrad's missus has been using a Nikon 1 then that may well not be an issue. What it sounds like is that she needs one of Nikon's superb macro lenses of which there are several choices. The new Nikon 1 would be a healthy upgrade from the 2011 version and it should be an easy transition from the older to the newer for her.

Correction: All Nikon 1 V1-3 cameras do in fact have an eye-level viewfinder which I suppose technically makes them DLSRs but without a straight optical image to view things since it's what is called a "mirrorless" rig. There are a number of such around now. I'm sure the V3 would be a nice upgrade but based on specs alone it doesn't seem especially necessary. Nowadays it seems that the appellation DLSR is as much about how a camera looks as it is how it actually operates. As an old dog I still prefer an optical viewfinder (can't use rear screens worth a damn) and my Canon T6s meets that case perfectly.

"Any suggestions on books or learning tools for her Nikon or learning how to "see the shot"?
No but what I can recommend is a screen shade to keep as much ambient light off it as possible. Shooting macro often means pointing the camera down and screen washout can make framing a shot a real pain. This shouldn't be a big problem if she's using the eye-level finder but the state of electronic viewfinders has improved dramatically since 2011 and that factor alone may be worth an upgrade.

NikonUSA website has lots of videos and information for the learning photographer. I strongly endorse it.

There is a type of camera called "bridge camera".

It's a superzoom camera with relatively large sensor. 1 inch.

And while it isn't as capable as larger format sensors you will notice

little difference if shot are taken outside in good weather.

They have a fixed lens, but the range is usually 24-600.

You might wanna stop by you local photo/video store and take a look

at those. They are just as expansive and entry mirror less cameras.

If your wife is happy with seeing shots on a smart phone, tablet, or computer the current Nikon should satisfy her. If she wants large prints then she will not be satisfied until she has a full frame DSLR. The number of pixels, while important, is not as critical as the size of the pixels in the sensor and how the information collected is processed.
And the down side of DSLRs is, the lens needed/preferred, is always in the bag, or worse, at home or back in the hotel. Less gear can make for a better photographer.
I could go on and on, as I am sometimes wont to. Feel free to PM me with a question now and then.