Castle Doctrine specifically protects you in a justified SD shooting, but that only applies under CD rules. If you are at Wal-Mart, you are not protected, for example.
In Wal-Mart you are protected under the Stand Your Ground laws or however you want to refer to them. If you shoot someone in a CD or SYG situation and are cleared by that DA and courts etc. this does not mean that the family cannot sue you. However their chances of winning are almost nil and they would have to either find a crazy lawyer or have a very unusual case to go forward with it. The CD and SYG laws say that you are immune from civil suits in such a case and it would be up to the suing party to prove that even though the DA and courts ruled in your favor that they were incorrect. Just say that the DA decided not to prosecute you for the shooting the family could then say that he was incorrect in his ruling and that he had bias against the dead person and all that kinds of stuff and they want their day in court. A ruling of a good shoot does not automatically take you off the hook.
If you were to go to trial with it and found not-guilty then you would have a very strong case even in civil court. If the family still decides to sue and the jury decides in your favor you can be awarded legal fees from the family.
Since most lawyers normally take such cases on a contingency basis depending on how much they win, seeing that it is unlikely that they will win the case they probably will require their fee up front. Seeing as how it is unlikely that the family (being non-PC here) probably have little to pay for a lawyer if he refuses to take the case on a contingency basis, it is unlikely that you will be sued. Your mileage may vary and IANAL.