When we found out that Bosco was diabetic it was do to a massive loss in his weight. He was obese and suddenly starting dropping weight but still eating large amounts so I brought him into work and had them do a urine test to find out what was going on.
There are several kinds of insulin out there for diabetic animals. All vary in price. We use Caninsulin as it's cheaper then the others. I don't know the price of the others off the top of my head. But we usually get 6 small viles of the Caninsulin at a time and it cost around $110 somewhere, we also get a discount so its probably higher then that normally.
Special food does help. We had Bosco on Purina DM, which is a vet food for diabetic cats. $55 dollars for a 12lb bag I think it was, which was insane so we switched Bosco to the Hills Prescription WD which just as well for Diabetic cats and costs way less and comes in a larger bag, again we get a discount on the WD so I can't give a price and the prices for everything vary depending on your area and from vet clinic to vet clinic. They don't need to eat just canned food (though canned food is better for cats) Bosco likes canned food but only every once in awhile otherwise he'll chose his Dry WD over his canned.
Your vet will prescribe you an amount of insulin to give for each shot (two shots a day).
Where I am the meters are free, it's the test strips that get you, for a bottle of 100 test trips it's around $100 somewhere. You'll also need a poker (at leats thats what we call it, the little gadget that pricks the skin to draw blood) I don't know if they are free like the meters or not. You'll have to prick the cats ear daily for the first little bit.
Some cats can and have grown out of their diabetes.
In a way we're lucky with Bosco being diabetic as my partner is also diabetic and has insurence to cover his medical needs. So the test strips and needles are covered and he splits up his stock of supplies with Bosco. We only pay for Bosco's insulin and food.
You can use insulin after 30 days as long as it hasn't changed color and has been kept in the fridge.
A site that will help with information is below. It even gives a list of good dry and canned foods that aren't vet foods so may cost less but still works well with diabetic cats.
I'm not sure why your vet thinks its diabetes though just from those symptoms unless he did some other tests that suggested it. Signs of diabetes are weight loss, lethargy, increased appetite, poor coat/hair, liver disease, infections becoming more adn more common, polyuria (large volumes of urine), and polydipsia (drinking large amounts of water). From the what we first told the vet she thought it was hyperthyroid which would have been giving him a pill every day for the rest of his life and far cheaper then if he had diabetes but... tests proved otherwise.
And your mother... she needs to suck it up and pay for the cats needs, if it had been you she would have no choice but to pay for it, just because its a cat doesn't mean it doesn't deserve the same rights. Though what she said about nobody wanting a diabetic cat is truth. Diabetic animals rarely get adopted as very few people are willing to pay for their medical needs. if the cat does have this it isn't a death sentance. My partner's mom has a cat who is 14 years old give a little more, this cat had diabetes and eventually just grew out of it, these cats can live long healthy, happy lives.