I hope you are able to resolve things with your Mum and keep your pup, but if not, then try to negotiate with her so that you can take the time you need to find him a home that will be suitable. I know this is a long shot, but depending on where you are, I have a good friend who is also a vet nurse, who often fosters dogs until she finds good homes for them. I'm in the Sydney area. There is also a Staffie rescue organisation - not sure if they take crossbreeds, but it's worth a try. They have a website. Perhaps you could find somebody on here you is able to help you with short-term fostering? Otherwise, give it some time and see if you get responses from on here for a new home. I absolutely agree that you need to be very careful who offers to take him while he is undesexed - lots of people see a pup like yours as a means to breed more puppies and make money, which is pretty sad. If you could ask whoever takes him to pay for him to be desexed first, if they agree, that's a good sign that they have the dog's best interests at heart and are prepared to look after him. I would also see giving him to a shelter as more of a last resort - many of them do a great job, but they don't have time to re-train puppies out of bad habits and the dogs have to go through the stress of being caged with limited attention and in unfamilar surroundings, which can make their behaviour worse. Many shelter dogs are very highly stressed and it can be traumatic for a puppy who is used to being at home in a routine. It sounds like you are prepared to do whatever it takes to keep your puppy, but parents can feel overloaded with the mess that baby animals make. It IS normal for all puppies to get into mischief, which is why they need a couple of walks a day, time at a dog-park (if there is one near you and he is fully wormed and vaccinated, including for kennel cough), etc. Perhaps the obedience club you mentioned will have somebody willing to help you and your Mum work things out?
Good luck and keep us posted about what happens.