My mother has me listed as a co-owner on stock certificates she holds. Your mother should review a list of her assets, their values and forms of ownership with an attorney to make certain that she understands potential tax liability as well as who will inherit specific assets.
Many people make logical assumptions about such matters and they are wrong.
An hour or two review with an attorney can buy a lot of piece of mind for a very small price. Estate taxes, by the way, are paid by the estate, not by beneficiaries.