Dear I am not proper diagnosed of your conditions due to insufficient information. But I trying to give you solution. In your tooth root first rct then put a post and core build up then bridging. But the success rate will depends upon the residual root structure, if it is shorter then it will fail in future. So it is well diagnosed then decided the treatment plan. And you told that she is suffering from cold sensitivity and tooth mobility. It means failure of rct. If mobility present then the prognosis was very poor.