Principium loquendi dominum in Osee is certainly very wrong Latin for the meaning that, according to both the KJV and the Douay-Rheims, it is supposed to have.
I've thought of a hypothetical explanation, though, but unfortunately I lack any evidence and I don't know how likley it is. I'll still explain it for what it's worth.
A few years ago, I came across an utterly ungrammatical construction in Aquinas, which was
cognitio existendi deum, supposed to mean "the knowledge of God existing, the knowledge that God exists". I posted about it on the forum and the conclusion of the ensuing discussion was that Aquinas had been translating from Greek, and had in this place translated a Greek construction in a nonsensical way. In Greek, you can take an infinitive or an accusative and infinitive clause and make this into a substantive by putting the definite article in front of it. The definite article will then decline according as the situation requires, and the infinitive or accusative and infinitive clause that follows it will stay the same. For example, το ειναι is literally "the to-be", i.e. "(the fact of) being", "existence", and το ειναι θεον literally "the God-to-be", i.e. "the fact that God is/exists", "God existing", "God's existence". Then you can only decline the το and make it e.g. genitive: του ειναι, "of the to-be", i.e. "of (the fact of) being", "of existence" and του ειναι θεον, "of the God-to-be", i.e. "of the fact that God is/exists", "of God existing", "of God's existence". The genitive definite article του followed by an infinitive alone can naturally enough translate to a genitive gerund in Latin, so
existendi is an acceptable translation of του ειναι (at least in medieval Latin, when
existo was commonly used with the meaning "exist"; this was rarer in classical Latin). But what Aquinas failed to realize was that even though
existendi worked as a translation of του ειναι, it became utterly nonsensical when the whole phrase was του ειναι θεον. In this phrase, the genitive article makes the whole phrase genitive (which is impossible to do literally in Latin), not just ειναι. Yet Aquinas translated του ειναι to
existendi as if it had stood alone, and then translated θεον to its literal equivalent, the accusative
deum, thus producing the ungrammatical phrase
existendi deum.
When I saw in the English translations of the Hosea verse that
loquendi dominum was supposed to be about God speaking (rather than speaking about God), you can see why I was reminded of the Aquinas construction, because it's strikingly similar:
existendi deum = of God existing;
loquendi dominum = of the Lord speaking. So I thought, could this verse have been translated from a Greek phrase similar to that translated by Aquinas? When I looked the verse up in the Septuagint, however, I saw that that construction is not used here. The Septuagint has a noun meaning "speech" followed by the genitive of the word for "Lord", a very straightforward construction and one that has a direct Latin equivalent, nothing that should have confused a Latin translator or led them to make such a mistake as Aquinas did.
Now my very theoretical hypothesis is that perhaps this verse was translated from some other Greek version that did have a construction like the του ειναι θεον one. Or, alternatively, but perhaps this is yet less likely, maybe mistranslation of the του ειναι θεον sort of construction was widespread enough at some point in a certain community that it was (horror!) actually adopted into common parlance and the translator of this verse just thought it sounded stylish here and decided to use it.
I also find it strange that the
Fornicabitur a domino
Translated to
Will be fornicated away from the Lord. A domino should be the ablative of agent here causing the fornication. That is not the case however.
Fornicari is deponent; it means "to fornicate" not "to be fornicated" (does the latter even make sense?).
Fornicari a domino = literally "to fornicate from the lord", i.e. to be unfaithful to the Lord, break his law, or the like.
It would be blasphemy to say that the Lord caused fornication.