No one is responsible for your mother's debts. Whether your mother lives with you or not does not make any difference. Only she is legally liable.
Since your mother has no assets she can probably eliminate all of her credit card debt with a Chapter 7 bankruptcy. I urge you to take her to a qualified bankruptcy attorney to explore this further.
With regard to the money that was spent on your brother's house, that is a more complex situation. This should be raised with the bankruptcy attorney to ascertain whether your mother has a claim against your brother that has any value. You should also talk to a general practitioner to ascertain whether your mother has a cause of action that she can bring against your brother.
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