Your sister is named beneficiary on the insurance policy - that is her money, period. She is not obligated to spend it on any of your mother's bills or other debts. Note, she's also not obligated to share it with anyone else - siblings, cousins, etc. It's all hers.
If there is no will, and even if there are no viable assets, there are still papers that need to be filed so that an administrator can be named, and Letters of Office issued. No titles can be transferred or property sold without the Letters of Office.
All assets not shared (that is, having someone named as owner with her) automatically become the property of "The Estate of ..." [insert mother's name]. Cars, bank accounts, homes, jewelry, etc. All that will be sold off and used to pay any debts owed by the Estate. These debts are given certain priorities - that is, some people get paid before others according to the laws in your state. MAKE SURE you go by that list. If you pay someone out of turn, the others have a right to sue the estate AND the administrator for mishandling the estate.
Please, seek the advice of a reputable attorney in your state, even if it's just a one-time consulting visit. Estate management can be done independent of an active attorney, but at least have them give you a detailed list of what needs done, where and how to file, deadlines for filing, etc.