Sounds like your argument is that the modification went through, you made payments, and now it's a done deal. If you lived up to your side of the contract, you may be able to win. Their argument is they thought they were dealing with your mother and that you were not eligible for the modification. Either of you could win, and then again, they could foreclose and let you present your argument in court. It's a pretty close case. I think you would be wise to get a lawyer involved to draft a letter saying you have an enforceable contract and they need to live up to it. You of course would have to provide all money that's due under the modification.
Get a lawyer now to assist you. The case law in NC has not been very homeowner friendly in terms of the mortgage world. you will need assistance in fighting this.