Since the house is titled to your wife and she actually receives the rent payments, the responsibility to report the rental income and expenses is hers. The fact that she deposits the rent into a bank account which is shared with her parents has no relevance.
Your wife is entitled to claim mortgage interest and real estate taxes that she was legally obligated to pay and which she actually paid. I hope that the arrangement with her parents at least leaves her enough money in the bank account to make those payments out of the rent receipts.
