OP I really am sorry this is happening to your family and I know it must hurt. However, it was not only yourself excluded but all your other siblings as well, except for one. So there is that comfort that you were not signalled out. I would not communicate with your sister anymore concerning the wedding, based on the text she sent you. She knows you are not invited and does not want to be straightforward and explain why. Awkward, especially when you say how close you are (or thought you were). There is no way I can believe that your nephew, a man in his 30's, does not know who is on the wedding list. Those lists are done and re-done so many times before the invites are sent out. The bride could not have prepared the list without his input and if he wanted you there, you would be on the list. So, he is, in my opinion, in agreement in not inviting his aunts/uncles/cousins whether it is by his in-laws request since they are paying or not enough space at the venue (or for any other reason).
I assume your sister knows you are your aunt's caregiver/helper and even then she was invited and you were not. What is there to say to them?
Honestly, I would not give them the satisfaction of looking like you are begging to go, that your feelings are hurt etc. and I certainly would never consider buying a gift for them. Listen you your dh and save your money for people who care.
P.S. Save all the money you would have spent on the gifts for the shower/wedding, new clothes, hairdresser etc. for your immediate family to attend and plan a nice little get away for your family. Money much better spent!