Ferrets can NOT roam the house freely with out supervision. Rule of thumbs: If their head fits their body will follow through. (IE tiny holes, open doors, broken screens, into furniture)
They love to poop in corners so you'll need a lot of litter boxes. (No corner is safe from a ferret) (They are usually good at 65%-75% trained)
They can easily get stepped on. They need a cage for when they are not going to be supervised. Ours get access to our room only and the rest of the house on a harness.
If your mother is allergic to cats she may be allergic to ferrets. I know many that are like that. Our friend can't be NEAR our ferrets due to his allergy to cats and them. He happes to have issues with rabbits or guinea pigs too.
I know many that have free roam rats, guinea pigs, rabbits, ferrets, chinchillas, and large reptiles.
You're best bet would not to get a free roaming pet. Get a parakeet. I've had several. They're fun, can be taught tricks, and are low on the allergy list. (Though its possible). I would stay away from difficult pets that are for advanced keeping. Large birds are loud, expensive to purchase, to treat medically (like ferrets) and need TONS AND TONS of attention. We know someone that has MANY large birds and they need someone willing to understand they are two year olds in a feathered body. Same as ferrets except the have fur.
Do your research have your mom make sure she isn't allergic to anything else. And any animal can be free roam as long as you're willing to watch it, and totally pet proof your home top to bottom. You're asking for too much. Most pocket pets will get into small places..Rabbits, chins, pigges, ratties, hamsters, gerbils, mice, snakes, ferrets. If your're worried about that with rabbits, forget anything small. Honestly the only two pets good at free roam (I saw pot bellies but most I know that have them keep them dog gated out of certain rooms) are cats and dogs. Even then most block them off from some places or rooms.