Its sad that she is more bothered about her own feelings then her pets
Can you not take him? will she allow that?
Also is she embaressed for him to see the vet or to take him out? Because you could always ask if the vet will do a home visit.
Im sorry to hear about this and I understand how you must feel, pets are family and its not nice when one is unwell.
You need to try and persuade your mom to take him to the vets, he could well be in pain