Hello everybody 
  
Thank you for all the good advice! 
To answer some questions, I am 13 years old 

 My mom is a stay at home mom.  
@BabieChloe: I think that might be part of the reason: I remember her saying once that when her dog died she was very sad.  
@HarrysMum: Thank you for giving me some added hope! Maybe my mom will agree like you did! We have quite a bit of money saved up from Christmas's and Birthday's so we could use that. 
  
@gemy: Do you think people would allow my sister and I to walk their dogs since we are minors? I think I might suggest that to my mom though! My sister and I applied to volunteer at a shelter but we haven't heard back yet. Hopefully they will soon!  
I think the reason why is the financial part and the fact that my mom lost her dog when she was younger. My aunt agreed that if our mom allowed us to have a dog that the pup could stay at her place until the pup is almost completely housebroken if my mom is afraid of the poop. Is this a good idea?  
Again, thank you for all the excellent input.