At another blog, 1 Peter, which I copy Mueller's position on the internal forum, there is another interview with Cardinal Mueller which he gave in the middle of December. In it His Eminence makes reference to the "internal forum."
I have written about this many times and a few years ago there was a lively discussion about it on this very blog, long before Pope Francis entered the scene.
In a nutshell, one cannot make use of the internal forum until the normal external forum is exhausted and no definitive decision about a contested marriage can be renedered due to a number of technicalities.
Fr. Kavanaugh might need to chime in on this if he remembers or was there. In the 1980's our now deceased bishop, Bishop Lessard, spoke at one of our clergy conferences (on St. Simon's Island as I recall) about the legitimate and illegitimate use of the so-called internal forum.
He made it clear that the external annulment procedure is the normal or ordinary form of accompanying a person who is in a marriage not recognized by the Church. This process had to be followed to its conclusion where a decision is rendered on the validity or non validity of a contested marriage. Of course, if the decision definitively states a sacramental marriage existed and thus it must be honored, there isn't much more than can be accomplished other than asking the Catholic to participate in the Church but without the benefits of the Sacraments (except in an emergency of course) or they should separate or at least live as brother and sister if the Catholic truly wants to receive the sacraments worthily.
Only if there is no possible decision that can be rendered because of technicalities, could one then use pastoral discernment based upon conscience to assist a Catholic to return to the sacraments without living as brother and sister.
As I recall, Bishop Lessard stated that the Catholic, not the clergy, should initiate the internal forum which is under the seal of confession (thus a priest must be the pastoral counselor). And one then can follow what Cardinal Mueller makes explicit in the interview I cut and paste below.
BUT IN NO WAY, CAN A MEMBER OF THE CLERGY OFFER ANY SORT OF PUBLIC OR PRIVATE CONVALIDATION OF THE MARRIAGE OR A BLESSING OF IT!
Here is what Cardinal Mueller states which backs up what Bishop Lessard told us: