My mom won't stop feeding my dog left-overs and expired food!?

Mom sounds like she has a screw loose. Is she really so wealthy that extra veterinary bills aren't a problem? Must be nice.
If you're old enough, move out. Or, clean out the fridge and cupboards of all old food and make it a point to throw out leftovers if she doesn't eat them the next day.

At 12 years old (or at any age) nutrition is very important. You want to make sure your dog is on a good quality senior food. My suggestions are Orijen Senior, Acana Senior, Blue Buffalo Wilderness Senior, Wellness Core Senior, or Now Fresh Senior dog food.

(If your dog is on a low quality food (Purina, IAMS, Science Diet,Pedigree, and etc) you may notice some gas, burbing, or runny poops for a bit - this is normal and should go away.)

You can give some people foods as treats, food you can feed are: raw carrots, any plain cooked meat (non-fatty), sweet potato, green beans, eggs, apples, flax seed, plain yogurt, peas, peanut butter, and most fruits/veg. Stay away from fatty, salty, sugary, or processed foods.

I know how annoying that can be! Good job for actually caring what you feed your pet.

Good luck! My 10 and 5 year olds are fed Orijen Regional Red with a wild fish oil supplement.

This is definitively bad for the dog, and he could develop a lot of problems due to this. Expired foods, salty, spicy, fatty foods are bad, as is dairy (a lot of dogs are lactose intolerant), onion, garlic, grapes, chocolate, caffeine, alcohol, avocado, nuts.

If she's going to give him anything it should be plain white pasta or rice, lean meats, and most fruits and vegetables (no seeds or cores). I honestly don't know what you can tell her though if she won't listen to you or your vet. Dogs react differently to food from one another, some have stomachs of steel while others are really sensitive, and with yours already having been constipated and bloated I'd say he doesn't tolerate it so well.

Dogs digestive systems are different than humans, but even so expired ham is not something you would eat yourself or feed a child. If he gets lots of fatty foods, he could develop pancreatitis (symptoms range from mild discomfort to internal bleeding and blood poisoning). Not to mention all the poisoning he could get if he's gotten dangerous foods. Some of these things build up a worse effect over time.

Try telling her that every dog is an individual, and that just because her childhood dogs were okay with eating old food, doesn't he will be. It is clearly not doing him any good at all. Otherwise, the vet would have advised against this.
Tell her politely that his health and safety is more important than any old traditions, family or otherwise. Campaigners against fox-hunting in Britain placed animals' lives over traditions when they fought against, and finally succeeded in banning, fox-hunting. Why can't we all follow their example and put animals before traditions and old ways?
It would be great if she could maybe keep a packet of good ham and/or other meats to give him as positive reinforcement, rewards and encouragement for training. That would mean that she would still be able to give him treats that are similar to what she would have given her childhood dogs without threatening his health and safety quite as much.
In answer to your other question, I don't know whether you will be able to get it where you live but, if you can, why not try him on some Burn's or James Wellbeloved dog food? This make has a really good reputation, and I have heard that either Burns or James Wellbeloved actually gives his own dog/s the food to feed it, to test new brands and because they enjoy the food.
Best of luck.

I wouldn't knowingly feed my dog expired food. I'd worry about getting food that old and not from a store, especially after all the petfood recalls they had a couple years back. A lot of people had serious problems, and the stores pulled the food, but you don't know if these samples might be of some of those foods. I'd just toss the food, it is less effort as well!