How many photos will fit on a 16 GB  iPad?
Short answer: 16GB should be fine for photos.

Long Answer: Your question is hard to answer with any accuracy as photos come in a variety of sizes depending on resolution, subject matter etc. For example, a photo taken on your 3GS iphone will be smaller than one taken on your 4GS iphone, which will also be smaller than one taken on your nikon DSLR digital camera. And as you could also reduce the image size based on how you want the photos to appear on your ipad, it becomes a bit more complicated to answer.

However, some math might give you a better idea at least.

1GB = 1024 MB so 16GB is 16384MB. Assuming you lose say 4GB for the in built apps and skype etc. we could say you might be left with 12GB or 12288MB. 

Let's assume your mother isn't a professional photographer with a 30 megapixel dslr camera, but for the sake of being conservative we'll say all of her photos are taken on a hi definition camera, like the iPhone 4s. Depending on a variety of factors the photo size will range from about 1.5mb to 3mb at full size (bearing in mind these are still HUGE photos at full res.) If we say 2.25 is an average photo size, you're still left with roughly 5,500 photos on your spare 12GB of space. 

Bearing in mind this is still pretty conservative the answer is that your mum can store literally thousands of photos in her 16GB iPad. If you weren't using a really hi def camera like the 4s iPhone, your photo sizes could be as small as 100 or 200 kb's each and the number is more like 50,000 photos. 

Hope that's helped.