Glad you understand that nobody can give you legal advice on this question. See this thread for more details on the disclaimer issue.
Just in case anybody else is listening, (or reading this thread), by posting to this thread, I’m not offering NinetyWt or anybody else legal advice. I’m not your lawyer, you’re not my client. Before you rely on anything that I or anybody else posts in this thread, you should consult an attorney licensed in your jurisdiction.
Having said all that, here are the relevant principles as I understand them. I caution you that I am not an estate planning attorney, so, if I get something wrong, let’s hope someone comes along and corrects me.
Here is the short answer to your question: you cannot be personally liable on a debt that someone else incurred simply because you are her heir. If your Aunt Sally dies, with $100,000 in debt, and she leaves you, her sole heir, $10,000, you–the heir-- are NOT on the hook for the other $90,000 that she owed when she died. On the other hand, you are not going to get the $10,000 either, because, generally speaking, all debts must be paid out of the estate before any of it can be distributed to the heirs. So, say that rather than leaving you $10,000 is cash, she left you a ring valued at $10,000. It is very unlikely that the ring will be distributed to you. Under our scenario, it will be sold to pay creditors.
When someone dies, a legal entity known as “the estate” comes into being. Debts incurred by the decedent are paid out of the estate. Whatever is left over is distributed to the heirs.
Student loans are kind of funny exception to this general rule. My understanding–and I’m honestly not sure this is right, it’s just what I heard–is that student loan debt, at least federal student loan debt, goes away on the death of the student who incurred the debt. In other words, in the scenario you described, the credit card balance would be paid out of the estate, but the student debt would NOT be, because it would be wiped clean on the death of the single parent. So, the children would receive the estate minus what ever was required to pay the credit card balances and minus whatever expenses were incurred to handle the estate (such as legal expenses, etc.)
NOW, there is AT LEAST ONE BIG EXCEPTION to everything I said above about being responible for someone else’s debts. If you AGREE to co-sign a loan or something with someone else, then you are on the hook. So, for example, say your sister co-signs your car loan, and you die, leaving your estate to your sister. Let’s say your estate is not big enough to cover the balance on the car loan. Now, in this case, your sister would be responsible for the debt. Not because she’s your heir, but because she agreed to co-sign your loan.