Go speak with your and her priest ASAP. There are a lot of steps before you two can be considered sacramentally married and therefore enjoy the marital embrace while still receiving Communion. I am not an expert, and my advice might not be free of mistakes, but here is a brief run-down.
Ideally, this should have been addressed when your wife became Catholic. Normally an investigation of previous marriages takes place before the Church will allow her to complete Confirmation and the Eucharist, but there are many situations where this is overlooked. I’m so sorry for you that you are in this situation.
In the meantime, it would be appropriate to live as brother and sister until this matter is sorted out, since it is far more important to keep one another out of sin and to receive the Eucharist. Basically each of her two previous marriages must be shown not to be sacramental before you can move to the next step, which is convalidation of your marriage. As someone has put it before, anything that has the appearance of the marriage is considered a marriage until it is proven otherwise, kind of like innocent until proven guilty in the judicial system. I THINK that if you were Catholic at the time of the wedding but did not receive a dispensation to marry outside the Catholic church, convalidation will be necessary.
Of course, all of this is much better addressed by a a priest who can consult Canon Law and determine whether the two previous marriages were sacramental. Pray, support one another, and be prepared for the very real possibility that one of her two marriages may be sacramental, thus excluding the possibility of bringing your marriage into the Church. I pray that this is not the case for you.