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If you had actually inherited this property, then your understanding would be correct. When you inherit property, you receive a stepped up basis in that property to whatever the fair market value is on the day you inherit it. If you then later sell the property for a higher price, you pay tax on the difference.
However, you did not inherit this property. Instead, your mother sold it to you for $1.00 prior to her death. Transfers of nominal dollar amounts are basically considered a gift, and gifts do not receive the stepped up basis. When you receive property as a gift, you retain the same basis as the donor's. Your mother's basis in this property would have been whatever she originally paid for the property plus the cost of any improvements she made while she owned it. That same basis passed to you at the time she gifted you the property.
Now if you sell the property your gain is calculated by taking the selling price less that basis, and that is the amount which is subject to tax. It would be taxed as a long term capital gain which currently has a maximum tax rate of 15%.
It is unfortunate that your family did not check in to the tax consequences of making this property transfer prior to your mother's death, as it would have been much more beneficial for you to receive this through inheritance and receive the stepped up basis. And even though you may have been named in her will to receive the property, the fact remains that she actually transferred the property to you prior to her death, and for tax purposes you will have to use your mother's basis when figuring the gain you have from the sale.
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Thank you keith