I'll say that there are many things that can go wrong and get you into trouble. I think the best that one can do is be properly trained and be aware of your surroundings.
You can't prevent every danger from happening. You can only minimise the incidence and the effects.
Also, engage reputable dive companies to conduct your dives.
Furthermore, if you feel unwell, uncomfortable or unsure about yourself or your surroundings or the dive companies' practices, don't dive.
Every sport has it's dangers. But if you learn how to mitigate them, they shouldn't occur. I've been diving for 8 years and the most dangerous thing that's ever happened to me was accidentally resting my elbow on some stinging hydroid and gaining a healthy respect for them after that. In fact, the worst thing that happened to me was not during a dive but during a snorkelling session - got stung by jellyfish.
I can understand that you want to respect your mum's wishes but diving is generally quite safe. Look at all the people in the world and throughout history that are still alive and well.