Can I not include some debts in a bankruptcy?
Generally no. Bankruptcy is an all-inclusive process, requiring full disclosure of all debts and assets. However, inclusion of a debt in your bankruptcy filing does not itself determine the final treatment of that debt. In chapter 7, reaffirming the debt is an option for secured loans (such as auto loans) on which you desire to keep the property and pay the debt. In chapter 13, some debts are candidates to be voluntarily paid in full in the repayment plan. In either case, a bankruptcy does not stop you from voluntarily repaying a debt (such as a family loan), it only stops your creditor for asking you for payment.
While there is some control over treatment of a debt, there are fewer options concerning keeping a bankruptcy secret from a creditor. Notice to a creditor that a bankruptcy has been filed is a core requirement of the bankruptcy process. For more about secrecy, please see Can I file bankruptcy secretly?