Do I have the right to invite myself to my cousins wedding?

Absolutely not.  People tend to very careful who they invite to their wedding, especially during the pandemic.  Besides, they would have to pick up your tab for the reception, which can be costly.  It would only be OK if your mom's invitation said that she could bring a guest.

No, it is incredibly rude to show up at an event which you haven't been invited to.

Only those named on the invitation are actually invited.  I've not sure your age here but if you're a child it's possible they aren't inviting any kids.  If you're an adult that doesn't mean you're welcome because your mom is.  

Many weddings/events also have assigned seating so if they are not expecting you to attend, there might not even be a seat for you.

If you were invited your name would be on the invite.

Absolutely not they may be on a tight budget 

why would you do that?

People do not gatecrash weddings. If they wanted you there, you would have been invited.