Thank you for the additional information in the So What Happened; it helps clear up some questions. I understand that based on your home society, your in-laws do expect financial assistance from your husband, and particularly because you are based in the US. That's the case with my in-laws also, and my husband and I have done quite a bit over the years. Just to clarify the responses you have gotten, remember that many of the people on the site are US-raised, so they have a different set of cultural expectations of siblings, in-laws, and parents. Americans might help their parents financially once they get really old and sometimes help a sibling financially in a pinch, however it would be the exception rather than the rule. So the people on this site can't really say if you are behaving selfishly because 'selfish' depends on the expectations. In American categories, you have been more than generous. In your home group's categories, maybe not.
In any case, I understand how the situation with your sister-in-law is difficult. You don't like her or get along, and there's no changing her or the history. Unfortunately, there's nothing you can do about the family gossip besides ignore it and be grateful you don't have to live next door. I wonder whether a good solution would be for your husband to be in charge of communicating any decisions about giving money to his family. Maybe the problem occurred because you were the messenger of the unwanted news? If you can take yourself out of the equation, then they can't blame you for the decision. Also, didn't you and your husband decide together about not giving them the additional money? If so, he needs to stand by that decision and tell his mother, brother, and sister-in-law that your family cannot give them that money at this point. It shouldn't be made into YOU refusing.
If the issue is that he wants to give more money to them than you feel your family can afford, that is a different problem. Perhaps you and your husband need to establish a budget of how much your family can give to relatives back home? Your family here needs to be taken care of, and life is incredibly expensive here, not to mention saving for the future. Set that budget of support for home, and once you reach that amount, your husband needs to say no, we can't afford it. There may be times when you have to exceed the budget, such as health emergencies, but otherwise, the answer is no. The issue is you two coming to agreement on what your family here needs and sticking to it. Good luck!