asking a parent or a sibling for money is normal, whether they rich or not.
Cousins and other extended family, nah. You just take pride in your uncle or whomever being successful, and at most maybe expect them to give a better wedding gift than everybody you invite to the wedding.
Think about it, how often do people normally borrow money from cousins normally? i got hand me downs from my cousins never any money. Maybe family discount if they happened to work in a store i was shopping in.
Edit: i will give a pass if the cousin you ask for money is also a legit friend. like a play cousin you hang out with all the time. but not some i see them once a year at the family reunion or thanksgiving type cousin.