Simply put, No, they will not know or be able to know you Blocked them.
According to Facebook's Help Center: (Here's the link, if needed: http://www.facebook.com/help/?faq=103802…
Will someone know if I've blocked them?
No. Blocking someone is completely confidential, and the person will not be notified that he or she has been blocked.
Although I don't know your specific situation, (your Yahoo profile says you're a 21 yr old male), I understand your privacy issues with your mother. Keep in mind, that IF you get caught, you need to be aware of the consequences. Prove to your mom that you're responsible to use Facebook. All the best to you. God bless