MaterDomini would be "mother of the Lord"
MaterDei would be "mother of God"
Dominicus = belonging to the Lord, a.k.a. "Dominic"
Dominici = 1st person genitive; "of Dominic"
mater = mother
Domingo is Spanish for Dominic -- it's also the name for Sunday, because it's "the Lord's (day)"
As an aside -- think about that: Spanish-speakers all over the world routinely call the first day of the week "The Lord's" instead of "Day of the Sun" like we English speakers. That goes for Spanish-speaking pagans, atheists, agnostics, you name it. The Catholic Faith is in their very language.
And of course there's "Adios" which means "A Dios" or "to God (with you)". The French have "Adieu" which means the same thing. I guess "Goodbye" could be a shortening of "God (be) by you".
Anyhow, I'm getting off topic.