Just how old are you? What sort of a neighborhood do you live in? Unfortunately this isn't the 50's when I grew up, and my parents expected me to walk places and later allowed me to ride my bicycle. Even then, we were cautioned not to talk to strangers, but there were very few problems. Today? It is a fine line between being overly protective and neglect. Perhaps your mother is showing wisdom.
When it comes to info on dogs, the net is a great repository of nonsense. I hate it when somebody that doesn't know enough to evaluate what they find, Googles up something. Quite often it isn't as good as what is in the sticky here. Sometimes rather than just being a weak or ineffective answer, it is actually dangerous. What you read may have been put up by some kook with an agenda.
Over weight is a big problem with dogs. It can be controlled both by reducing a dogs chow, or increasing its exercise and a combination of the 2. I would disregard anything else you read on the website that said reducing the food wasn't enough. I have enough experience and training to evaluate what I find on the net. I can say you will find reliable material at
LongLiveYourDog.com - Life Span Study - Rate Your Dog It is the same system as I have been trained to use for years on the puppies I raise for a large dog guide school. They are in a position to know what is good for dogs, and have every incentive to give straight answers to those caring for their dogs. I trust what Purina says when it agrees with what I know is a reliable source.