Eek I would be terrified of a Praying Mantis lol! That is sad if your Mom is afraid of animals. I would second showing her some cute videos of hamsters. You could also say that you would do all the care for the hamster, and the hamster would only ever be in its cage or in your room if out of the cage.
First thing though is do loads of research - so if you do get one, you get everything right before getting the hamster. Lots of people make mistakes and aren't prepared as pet shops give bad info sometimes - partly because they don't know much about hamsters, or because they are in the business of selling cages (whether suitable or not).
So you need to think about where you would keep a hamster, would you have enough space for a large cage (at least 80cm by 50cm continuous floor space- ie in one cage space). If you can afford a cage big enough, or whether you would need to make a bin cage or a diy cage. And whether you'd have enough time to care for the hamster and give it enough attention etc. Which I'm sure you have.
Getting the cage and wheel right are important though. Syrian hamsters need a safe wheel with a solid running surface, of about 11" diameter - so a cage needs to be tall enough to fit that, but not too tall or it can have injury risks from falls as hamsters can climb right to the top and then drop (they're not good at climbing down).
Do you know why your Mum is afraid of animals? Maybe you could talk to her about that and ask her to explain to you. It may be she was once bitten by an animal as a child or something. You could say that hamsters are only very small and that they bond with a human owner and are clean little things who wash themselves and will use a litter tray, and very amusing to watch. And then show her some videos.
Have you thought about what kind of hamster you want? A Syrian is often easier for a first time owner, as they can be easier to handle and tame and less likely to get injured (big generalisation there but a Syrian is often recommended for a new owner). Dwarf hamsters are very tiny and it can be nerve-wracking for a new owner.
Your Mum may also be worried that you'll get bored quickly and she will end up having to look after the hamster!
My other half didn't want us to have a hamster either - he is scared of rats and said hamsters were a bit like rats. He doesn't think that now and likes our hamsters
He still won't let us have a pet rat though haha!
I think you need to be a little bit patient and win your Mum over to the idea - and be prepared to do all the care yourself.