Yes, it is cruel to punish a dog in this manner.
Most likely, he doesn’t associate his crime with the punishment, and thinks your mother is just being mean for no reason. Dogs have extremely short memories for cause and effect. Unless you punish * immediately * when catching him doing something wrong, the dog does not associate his behavior with the punishment. Even a delay of a minute before punishment can cause a dog to be extremely confused. Hot sauce will not help in any way, unless it is placed on an object that you don’t want him to chew, but even then, I’d suggest something like “Chew Stop” because hot sauce is painful and lasting. Dogs do not understand long punishments.
I suggest that you get a crate for the dog. When you’re not at home to watch him, leave him in the crate. When you are home, monitor his behavior carefully. Correct with a sharp “NO!” when you see him doing something wrong.
You may want to put a bell on him. When my dog was a pup, I put a bell on her collar. I could keep track of her movements, and if I heard the bell stop jingling, I knew she was up to no good.
If he has stolen something to chew on, take it away, and give him one of his own toys. When he starts to chew on that, praise him. This way, he will learn what is his.
Put the food where the dog cannot get to it, or buy a container that he cannot break into. Perhaps he was starved by his previous owner, and doesn’t yet trust that food will always be available to him.
An abused dog is going to need extra love and patience. He really wants to be a “good dog,” but doesn’t yet understand what you want. He will need lavish praise when he does something right, and gentle correction when he does something wrong. When you catch him being a “bad dog,” distract him, rather than just punish. As an abused dog, correction will frighten him, so it should always be tempered with praise. You can either give him a command that he knows, such as “sit” and then praise him when he does it, or take him to another room and play with him.