Yes it will be the shakey camera that is leading to the photos getting blurred.
If the shutter speed at which your camera operates at is too slow, any vibrations of the human body, including natural shaking motion that occurs when holding the camera, will cause this. The shutter speed may be slow if there is not much light because you’re using a large focal length, or if it is just too dark.
To prevent this you can tell her to try and adjust the shutter speed. The general rule is to use a shutter speed that is at least as fast as 1/focalLength. e.g. if you’re using a focal length of 100mm then the shutter speed should be at least 1/100th second.
Adjusting the shutter speed is not always an option, especially with cheaper digital cameras. So, in this case I would advise using some kind of support, such as a tripd or monopod. Monopods don’t offer as good and steady support as tripods, but they are lighter, cheaper and easier to carry around. And, as you’ve suggested, a remote release is another option. You can get cable attached or wireless remotes. These also have the advantage that you can trigger the shot from different vantage points, and don’t need to be directly behind the camera.