Is my uncle's sacrifice sufficient on my behalf, or must I sacrifice myself, and what should I do about the past years in which I did not sacrifice?

The Udhiyah (sacrifice) is sufficient for its owner and his household whom he supports. If your uncle does not support you, then his sacrifice is not sufficient for you. It is permissible for you both to share in a sacrifice if it is a camel or a cow, but sharing is not permissible for a sheep. You should offer a sacrifice for yourself and your children, even if you live in your uncle's house. You are not required to make up for what you did not sacrifice in past years, because the Udhiyah is a confirmed Sunnah according to the majority of scholars.