In my opinion, Joe gives the money to his wife because she is the dominant force in their relationship. I think that Dickens has him do this as a way of showing us that she is really the one who is in control. When Miss Havisham gives the money to Pip, she tells him to give it to his master. He gives it to Joe. When Joe gives the money to Mrs. Joe, it implies that she is his master.
Throughout the early part of the book, we see many things that show us that Mrs. Joe really controls Joe. This is one of those bits of evidence of her dominance.