I think I'm going to have sex at home to intentionally get caught by my mom.
I cannot believe what you are saying! Why would you want to get caught by your mom?
I just want her to know that I'm not a kid anymore.
Wanting your mother to know you're an adult is fine but trying to get caught having sex to do so it a bit weird. I feel like that would have the opposite affect and your mother would think that you're immature in fact. If you set this up without your partners consent as well then it's just outright wrong because you're knowingly embarrassing for your own goals.
I'm going to do it since I was planning to have sex with her friend and she doesn't like me.
There is a lot going on with this situation and it is all wrong. You need to be dating people your own age and keeping your relations private.