Thinking about what aussieJJDude wrote above, I got to thinking about some of the more, we'll call them 'creative', things I did when younger to get what I wanted. I'm not gonna write about that here because I don't want to seem to endorse dishonesty (I was extremely dishonest... kind of a nightmare for my parents, really
)
But I remembered something that once worked - I did a written assignment (with diagrams) about rat respiratory tract infections, so my parents would shell out for the more expensive bedding they needed, after discovering that the cedar shavings I'd bought them were a serious irritant. I was out of money (and the grass wasn't going to need mowing for at least another week... also, I did not have permission for the rats i had aquired, so this was all really a bit much for my poor parents.)
My parents really valued school work, & education* (*and I was a very poor student geneally), so putting together a written project was effective. I got my English teacher to help, and she even allowed it to be worth extra credit. (A science teacher might do as well.)
If you want to give this a try, I wouldn't mind supplying you with a bibliography, references, and/or editing. You could create a project that details their life in the wild, how they moult, or whatever you think might be helpful for your mum to read.
Its a long shot, I admit - but it might be more convincing than just saying facts, if she saw that you had put a bunch of extra work into the argument. Getting a teacher on board to say "yes, what a good paper HermitCrabGirl03 has written, clearly a future marine biologist" (or whatever it is teachers say to impress parents), could be helpful too if she's the kind of adult more easily influenced by other adults.
Finally, I recommend thinking strategically. ... everyone has things they value: be it money, social standing, comfort, aesthetics, or whatever. Comming up with ways to tie the outcome that you want to something your mum thinks is useful or good will improve your chances... if you try to think like her maybe a new idea will hit you.
Why did she allow you to get hermits in the first place? What did she think about them?
why would... What? Why would they take away there toys/food and water bowls. I hate to say this but, (maybe they are trying to get you to get rid of them)... That is just cruelty to animals. I know people think hermits are stupid pets.. It's just unfair.