Does the Catholic's Trinity doctrine imply that the Unitarian God Multiplied into Three persons by Generating the other Two?

let's look at the original text:

The Lord says, “I am the Lord your God, who led you out of Egypt. You have no God but me. I alone am your savior. Hosea 13:4 GNT

here clearly state there is 'no God' but God of Israel, and 'alone'. i think there is more than 50 verses that contains similar wordings that shows there isnt any other god(s) than God of Abraham, Isaac and Jacob.

Hope God had given the best introduction of HIMSELF to the world to know.

No, it does not. The Trinity, as taught by both the RCC and by Eastern Orthodoxy, is a divine mystery ultimately incomprehensible to human nature (necessitating Faith for our knowledge of it at all). For the West it is best expressed in the Athanasian Creed, which states

...And the catholic faith is this: that we worship one God in Trinity, and Trinity in Unity; neither confounding the Persons, nor dividing the Essence. For there is one Person of the Father; another of the Son; and another of the Holy Ghost. But the Godhead of the Father, of the Son, and of the Holy Ghost, is all one; the Glory equal, the Majesty coeternal. Such as the Father is; such is the Son; and such is the Holy Ghost. The Father uncreated; the Son uncreated; and the Holy Ghost uncreated. The Father unlimited; the Son unlimited; and the Holy Ghost unlimited. The Father eternal; the Son eternal; and the Holy Ghost eternal. And yet they are not three eternals; but one eternal. As also there are not three uncreated; nor three infinites, but one uncreated; and one infinite. So likewise the Father is Almighty; the Son Almighty; and the Holy Ghost Almighty. And yet they are not three Almighties; but one Almighty. So the Father is God; the Son is God; and the Holy Ghost is God. And yet they are not three Gods; but one God. So likewise the Father is Lord; the Son Lord; and the Holy Ghost Lord. And yet not three Lords; but one Lord. For like as we are compelled by the Christian verity; to acknowledge every Person by himself to be God and Lord; So are we forbidden by the catholic religion; to say, There are three Gods, or three Lords. The Father is made of none; neither created, nor begotten. The Son is of the Father alone; not made, nor created; but begotten. The Holy Ghost is of the Father and of the Son; neither made, nor created, nor begotten; but proceeding. So there is one Father, not three Fathers; one Son, not three Sons; one Holy Ghost, not three Holy Ghosts. And in this Trinity none is before, or after another; none is greater, or less than another. But the whole three Persons are coeternal, and coequal. So that in all things, as aforesaid; the Unity in Trinity, and the Trinity in Unity, is to be worshipped. He therefore that will be saved, let him thus think of the Trinity.

To our human minds the above contains contradiction after contradiction (Trinity in Unity and Unity in Trinity, etc.). So Pseudo-Athanasius explicitly corrects any possible errors that may come in our understanding, e.g. by reminding that there are not three eternals but one eternal. This is faith which is believed requiring the infused virtue of Faith whereby it is believed.

Asking about Catholic/Orthodox doctrine suggests a desire to understand the doctrine. If the question seeks an answer that criticizes the doctrine, that is another matter. My answer will be based on the first suggestion. One does not have to agree with the doctrine to understand it.

Catholic doctrine rejects the idea that there was ever a "Unitarian God." The divine "economy" takes place in eternity, outside of time. In this view, to apply temporal categories to the process takes it back inside time. For trinitarians, to speak of multiplying the unitarian God is blasphemous. The word "generation," however, is sometimes discussed. No less an authority that Thomas Aquinas admitted to a type of generation in the Godhead, although he was careful to point out that it was not an "outward" creation, but an inward procession:

It was left to St. Thomas to clarify the exact nature of this generation. In the Summa, he explains two types of procession. One is an outward act of creation, while the other is an “inward procession corresponding to the act remaining within the agent.” This second kind of procession is purely an act of the intellect. If you have a thought, that thought may proceed outwards and become manifested as words or actions, or it may proceed inward as a “conception of the object understood, a conception issuing from our intellectual power and proceeding from our knowledge of that object.” - From Generation and Spiration: The Processions of the Trinity by Thomas L. McDonald

The OP is correct when it says "the language and these phrases in their creeds have resulted in confusion and debate." However, trinitarian Christians would not agree that "One might even say that such a literal generation of the divine persons undermines the doctrine of Immutability or the unchangeable nature of God." For "orthodox" trinitarians, God exists outside of time as an eternal Trinity, which is, in itself, the immutable nature of God. Again, one does not have to agree with the doctrine to understand it.