I have yet to finish reading Mulieris Dignitatem, but I have read the shorter recent CDF document on the Collaboration of Men and Women, which indirectly refers to the issue of "mutual subjection", as has been discussed in a recent post. The way I am reading it, the phrase "mutual subjection" in the former document seems to be used in the same context as "collaboration" in the latter. In fact, a case could probably be made that the expressions are interchangeable. Rome seems to have made a decision, more or less explicit, that since the phrase "mutual subjection" has a clear hierarchical implication, potentially conflicting at that, they have rather substituted the word "collaboration", which has a greater chance of being understood in the manner intended.
So, taking the word "collaboration" and projecting it backward onto Mulieris Dignitatem is a useful exercise. In fact, that document, as well as the comments others have made, become abundantly clearer, when understood in this way. When trying to force a new meaning onto an existing word, there is bound to be misunderstanding, as with the phrase "mutual subjection". As Scripture and many other sources make clear, to be "subject to" someone has an objectively hierarchical implication. No matter how frequently or forcefully it is repeated, it is simply incomprehensible how two people could be subject to each other in all things. It makes a mockery of the word "subjection", in the way it is normally understood.