AnimalLover, tell your mum that I can totally sympathise - I am an animal lover and vegetarian too and pet food is a problem. However, there is no other way for bettas to survive - they are obligate carnivores and their systems simply cannot digest vegetable matter. As a result, a meaty pellet such as New Life Spectrum or Omega One is very important for this fish's health.
As an animal lover, I'm sure your mum will agree that it is important to keep a pet in the best circumstances possible, or it isn't fair to keep them at all. Bettas don't come from the ocean - they come from slow-moving bodies of water in Asia. Sure, they don't need heaters there, but that's because the water is consistently warm. In the US, it isn't, so a heater is very important.
Bottled water is also not ideal (if your bottled water is like ours) as it is stripped of minerals that the fish need. Tap water with a water conditioner will keep your fish healthy.
Please explain to her that if she won't let you provide your fish with what it needs, it will actually *be* animal cruelty, and that will be against what she believes in.
A general note: guys, AnimalLover's mum may be causing problems for his/her fish, but let's keep it polite, hey? :)