Let my just cite one (of several) occurrences in the psalter, and compare the translation of verse 3 as presented in the New American Bible, the Douay Rheims, and the underlying Vulgate.
NAB - Let them praise his name in dance, make music with tambourine and lyre.
Douay Rheims - Let them praise his name in choir: let them sing to him with the timbrel and the psaltery.
Vulgate - laudent nomen eius in choro in tympano et cithara cantent ei
So, full disclosure; I am not a Latinist, but rather one who wishes to understand what God through the agency of the scripture, the product of a human author through the agency of the Holy Spirit has to say to me. Unfortunately, I do not know the original language, and there are translators between me and the original inspired text. Hence, I may be receiving, in places, the bias of the translator rather than the inspired word of God.
I do know enough to know that the Council of Trent has declared the Latin Vulgate to be inerrant (as opposed to inspired) in matters faith and morals, and the sure guide to resolve differences of opinion. I only mention this, because the word in question, "choro", comes to us in the Latin Vulgate, and the translators have variously brought that forward into English, as either "dance" or "choir", both of which are found as translations in Latin/English dictionaries in common use over the last two centuries. Then again, there is a certain bias in the order different dictionaries present translations, the order not necessarily reflecting common usage.
What I'd like to suggest, is based on a look at St Augustine's commentary on the Psalms. Now admittedly, what we see today is a translation of the his original work, but what is compelling is that the translation clearly indicates he understood the meaning in terms of a choir of singers, not a troupe of dancers. Try to shoe-horn "dance" into what follows, and it becomes nonsensical.
St Augustine, Expositions on the Psalms
- 4. “Let them praise His Name in chorus” Psalm 149:3. What means “chorus”? Many know what a “chorus” is: nay, as we are speaking in a town, almost all know. A “chorus” is the union of singers. If we sing “in chorus,” let us sing in concord. If any one's voice is out of harmony in a chorus of singers, it offends the ear, and throwes the chorus into confusion. If the voice of one echoing discordantly troubles the harmony of them who sing, how does the discord of heresy throw into confusion the harmony of them who praise. The whole world is now the chorus of Christ. The chorus of Christ sounds harmoniously from east to west. “Let them sing a psalm unto Him with timbrel and psaltery.” Wherefore takes he to him the “timbrel and psaltery”? That not the voice alone may praise, but the works too. When timbrel and psaltery are taken, the hands harmonize with the voice. So too do thou, whenever you sing, “Halleluia,” deal forth your bread to the hungry, clothe the naked, take in the stranger: then does not only your voice sound, but your hand sounds in harmony with it, for your deeds agree with your words. You have taken to you an instrument, and your fingers agree with your tongue. Nor must we keep back the mystical meaning of the “timbrel and psaltery.” On the timbrel leather is stretched, on the psaltery gut is stretched; on either instrument the flesh is crucified. How well did he “sing a psalm on timbrel and psaltery,” who said, “the world is crucified unto me, and I unto the world”? Galatians 6:14 This psaltery or timbrel He wishes you to take up, who loves a new song, who teaches you, saying to you, “Whosoever wills to be My disciple, let him deny himself, and take up his cross, and follow Me.” Matthew 16:24 Let him not set down his psaltery, let him not set down his timbrel, let him stretch himself out on the wood, and be dried from the lust of the flesh. The more the strings are stretched, the more sharply do they sound. The Apostle Paul then, in order that his psaltery might sound sharply, what said he? “Stretching forth unto those things which are before,” etc. Philippians 3:13 He stretched himself: Christ touched him; and the sweetness of truth sounded.
So even if we were to stipulate that the better translation is "dance", it remains a term that in English is much broader in meaning than the literal translation from classical Latin, which is a very limited subset of "dance" as understood in modern English, where it covers everything from a 1940s Broadway musical "chorus line" and a "square dance" all the way to a "pole dance". Since some parishes have devolved to the point of homo-erotic dances at Mass more akin to the last listed, it is my regret that the word was not simply transliterated (and left as "chorus") rather than be written as "dance", as it was in the Douay Rheims.
So dear Holy Father, if there is any schism, do consider that it is not a thing defined in political terms within the Church as she stands, but is rather between the Church Triumphant (and Suffering) and a significant part of those who are the Church Militant. And with a hat tip to canonist Ed Peters, no, this is not a schism per canon law, but one of the heart, as indeed I think the Holy Father (not one for canon law) sees it.