Hello and welcome to HC!
As everyone has already said, as much as it's going to suck, you have to respect your mother's wishes. When I was young, I wanted a hamster so bad, and I thought I had done a lot of research on them when in reality, I knew little to nothing about them and a majority of the information I did have, was incorrect! Luckily, she never allowed me to get the hamster and I'm so glad she didn't as I never have to live with the shame of keeping any hamster in a cage that was too small with improper care. Sometimes parents really do know what's best and it may not be something you see now, but can see later
It sounds like you really love hamsters, and luckily for you, not being able to own one doesn't necessarily mean you can't be with them! You can spend time researching and advocating for the betteremant of their care. You could also volunteer at a shelter or small pet rescue so you can get exposure to them and get to bond with them. Not only will you get exposure to hamsters, but you'll also be supporting a wonderful organization and what could be better than that? I too think you should research more before breeding. More goes into it than simply putting two hamsters together! You have to have extensive knowledge of genetics, colors, coat types, behavior, and genetic disorders. All of these things are very complex and can take years to learn. Besides that, realize that birthing is hard on female hamsters, is it worth the risk of your female hamster dying just so you can bring more pups into this already overpopulated world? It's going to cost hundreds, if not thousands to start up breeding as well. Each hamster will require his/her own cage and each can run over $100 for only the cage. Then factor in toys, bedding, food, wheels, bowls, and water dishes and you're at around $600 for about 2-4 hamsters. Then you've got to purchase a pair of high quality breeders, and this can cost $50-$100. You'll also need to have a bare minimum of $500 stuffed away as an emergency vet fund. There's more to it than just price though as I mentioned earlier, learning genetics and knowing how to recognize good health and temperaments is crucial and is a skill not everyone can master. Being 17, you'll also need to realize that you may be going off to school soon or getting a job, and all these things cost A LOT. It may be best to consider only keeping 1-2 hamsters until you're all done with this and know for sure you'll have the funds and knowledge to partake in breeding.
This wasn't meant in any way to sound harsh, just something to consider! In the end, it's your choice and there's nothing we can do to stop you, but you should do lots of research at least before getting into this. Hope to see you around the forum