First of all Hamsters dont smell. Your mother is poorly misinformed. Hamster urine isnt nearly as potent as a rats or mouse.
Cleaning the cage once a week will eliminate any strong smells. People that take poor care of their hamster cages are going to be the ones that smell.
Another thing you can point out to your mother is that hamster can be potty trained. All you need is Chinchilla sand and a shallow box or container to put it in. If you place it in the corner your hamster chooses to urinate in this will help eliminate odor and you can change this every 2-3 days.
Most hamsters have a corner they choose to urinate in. This is what smells the most I find, not fecal matter.
You could also try a large sized aquarium to help retain any smells that might bother your mother. But these are more awkward to clean because of their shape and their weight. Dont put a Syrian in anything less then a 29 gallon.
But really if you provide a potty and change the cage once a week the smell shouldnt even be an issue. Carefresh, Yesterday's News and CritterCare bedding is very absorbent and more ideal for your hamster. You can see more about bedding and pottys
HERE
Before you do get a hamster though its best you have a talk with your mother and have her agree to take the ham to the vets if it ever needs it. Saying its not worth it because the ham cost 10 dollars is a very poor excuse. Unless of course you are already able to afford this yourself.