Canon law states:
The obligation of assisting at Mass is satisfied wherever Mass is celebrated in a Catholic rite either on a holy day itself or on the evening of the previous day (canon 1248 §1, Code of Canon Law, emphasis added).
What this means is that a Catholic may satisfy his Sunday/holy day obligation at any eucharistic liturgy celebrated in a Catholic rite. The eucharistic liturgy that you attend does not necessarily have to be one that specifically celebrates the solemnity honored by the holy day.
What you cannot do is try to fulfill both obligations (for the Immaculate Conception and for the second Sunday of Advent) with one Saturday evening vigil Mass on December 8. If you choose to fulfill the Immaculate Conception obligation by attending a vigil Mass on Saturday (which will be dedicated to the second Sunday of Advent), you must attend another Mass either later that night on Saturday, or on Sunday, December 9 (which will also be dedicated to the second Sunday of Advent).