It sounds as though you really need this surgery. And it doesn't have to be heart surgery to be important. I think you need to concentrate on getting your surgery taken care of
and then work on your recovery. I know this is not pleasant to think of but you will most
likely have pain. And you may need some medication to help control your pain. I don't see how you will be in any condition to go each day and take care of your dad's dog.
I think you need to have a talk with your sister, tell her you must only concentrate on yourself during this time and take the help that your boss or friends are offering you.
If your sister is so worried about the dog then she can go over and take care of it or there are countless dog walking and sitting services that she can hire. Why can't she take the dog to her house? You are not causing any one problems. You are the one who has the problem which is you need your
surgery. Anyone who is making you feel bad or guilty about this is not showing the proper concern and caring that you deserve. How does your sister think you will get to
your dad's house? I doubt you could drive. I think it needs to be very clearly explained to your sister exactly what your surgery involves which is a lot and that if her area of help is with your dad then she must help him including taking care of the dog. Your boss is willing to help you and take any help your friends can provide. Please don't cancel your surgery. I feel that anyone who thinks you are causing problems is someone who is covering their own feelings of guilt for not coming to your aid.
Please post and tell us how things are working out.