My mother had fluid removed from around her heart on May 13, 2012. The Dr. caused additional bleeding that resulted in her death. He had admitted this

I am assuming that the procedure your mother had performed was a pericardiocentesis. Was it being performed for diagnostic purposes or was she being treated for a cardiac tamponade? this would be important, because in North Carolina a different standard of care applies to emergency services.   In either situation, because this is a invasive procedure, there is a risk of damage to adjacent organs and structure. Was an autopsy performed? having that information would be helpful in deciding whether her death was to medical malpractice.   I would not necessarily infer negligence from the fact that the hospital has made some offer. Furthermore, any offer made by the hospital would be inadmissible in court as evidence of liability. The stature limitations in North Carolina on a wrongful death action is two years from the date of death. The only way to determine whether or not you have a case would be to obtain complete copies of your mothers medical records and have them independently reviewed.