Providence

Thomas Tucker, if the school is the one I think it is, I imagine such differences are handled very gently, given that the tuition is $8K or so per year for the elementary grades. That's not a snark, btw. One of the reasons I homeschool rather than send my children to parochial schools is that where I live, parochial schools are more like private schools and less like religious schools; that is, they charge very high tuitions which ensures exclusivity (whether it's intended to or not) and they accept relatively high numbers of non-Catholic students, both of which have an effect.
My parents complained long ago about some aspect of the religion program in the Catholic school I was attending; it was doctrinally weak to the point of being practically indistinguishable from Protestantism. Their complaint was answered with shocked looks, and a statement to the effect that the school wouldn't want to "overdo" the Catholicism, as the non-Catholic students and their parents might be offended (and take their money elsewhere, one could infer). The situation has only gotten worse from what I hear. That said, I'm not criticizing those who do send their children to private religious schools. Such schools quite often provide a good environment for quality academics and the sharing of some common values. Just don't expect them to be bastions of Christian orthodoxy (large or small "o").

"I would say without a shadow of a doubt that Providence is a bastion of small-o Christian orthodoxy." That's wonderful, if true, but I honestly don't see exactly how it can be. Orthodoxy in both the Orthodox and Catholic traditions doesn't include 'sola scriptura;' it does include capital "T" Tradition and a rich sacramental life. I suppose having been educated more like a Protestant than a Catholic in my elementary school years it's hard for me to see exactly how such important omissions can be considered orthodoxy--particularly since the Eucharist, the central transcendent reality of both our faiths, must necessarily be downplayed when the school's own religious tradition sees it merely as a memorial and representative meal, not as the literal presence of Christ in our midst.
Granted, these deeper theological realities won't cross your son's radar for several years, but speaking from my own experiences I'd be concerned about a dual presentation of Christianity which is one thing at school, and quite another at home. For myself, though I'd heard certain words and phrases in school all my life, it wasn't until I was in the eighth grade that I learned the term "transubstantiation," and, further, was able to internalize what it meant. I still remember going to Mass shortly after that and being really aware, for the first time, of the incredible and awe-inspiring nature of what was happening there, and Who it was I was receiving. And this happened in a Catholic school environment, where such omissions that occurred were the result of carelessness of catechesis, a spirit of false ecumenism, or that nebulous agenda known as the "Spirit of Vatican II."
That said, please don't take this as criticism of your, or anyone else's, personal family decisions regarding education. We do the best we can, as parents, after all.

Amen, Rod! A brief story that might amuse you. My wife, my 13-year old son, my 15-year old daughter, and I went on vacation this past weekend. We were on the bus that takes you from the Miami airport terminal out to the small plane that flies to the Bahamas. The kids noticed a truck with a tank labeled "potable water" and got into a discussion of the root of "potable." My son wondered whether the root was actually from Latin because he knows that "bibere" is the verb "to drink." He was, btw, carrying a fat tome about the Roman Empire (which he read much of on the beach). At this point, the lady standing next to us on the bus asked if we were homeschoolers! I certainly took this as a compliment.
Providence, along with the families whose children go there (and I want to specifically credit my kids' mother, always an avid reader), does a great job of turning out kids who love to read good books. My daughter (who went to Providence through 8th grade and is now at Highland Park) brought, and finished, C.S. Lewis' Till We Have Faces, plus Oswald Chambers' My Utmost for His Highest, which she has been reading day by day this year. That school is wonderfully orthodox and very strong academically. It has been such a blessing to my kids -- and, I'm sure, to their younger brothers as well.