Is the death of the husband's relatives after the questioner's childbirths related to the matter, and is she sinful because of that?

You are not to blame for what happened to your paternal uncle's wife, for it was by God's decree. Your attempt to prevent pregnancy out of fear for her falls under the prohibited ṭīrah (superstitious omens). Ṭīrah is pessimism arising from something disliked, whether a saying, an action, or something seen. The Sacred Law has invalidated and forbidden this. It is polytheism (shirk (definition)) because it involves believing that it can benefit or harm, or that it can bring benefit or ward off harm. Therefore, you must stop taking birth control pills and rely upon Allah Almighty.