I'm sure someone who knows more about this will correct me, but I thought you weren't supposed to have communion services on weekdays, or really at any time except when there wouldn't be a priest at Sunday Mass.
Also, from the USCCB: "When daily Mass is scheduled in a parish, it is usually not appropriate to schedule a Liturgy of the Word with Distribution of Holy Communion."
Also, woman or man, there should not have been anyone "leading the service" as far as I can tell.
So I tend to think that a) if there were two Masses that day, there should be no communion service, and b) even if there were to be a communion service, there should not have been someone leading it (unless it were a priest or deacon).
From a quick look at a couple of documents, it seems like the general idea is that if you can't attend Mass at your own parish, you should find a parish where you can attend Mass, unless that is impossible (because you are too poor or too sick or something).
But since the practice is discouraged rather than prohibited, really your best option would be never to attend another of these services. If the parish advertised Mass, and then had this instead, that would be a serious cause for complaint. But if they advertised it for what it was, and you chose to attend it, the only real cause for complaint (and I'm not saying it's small) was that the wrong words were used. However, unless you happen to have a copy of "Holy Communion and Worship of the Eucharist Outside Mass" it will be difficult to give specifics of what was wrong. I wasn't able to find it online, although I did find the following which does not strictly apply but does seem relevant:
So yes, you were right to feel uncomforable, but no, there is probably nothing you can/should do about it, except next time, either get yourself to Mass, or (since Ash Wednesday is not a holy day of obligation) stay home.