Wrong. And it is wrong to do so. These Jews are secular, or subjugated to Islam. It is nor okay for Jews to call their God by the name Allah, because it denotes dhimmi status to Islam. Yes, it technically translates as "the god" but the god is not OUR GOD, not if it's translated from another language. This would be like some Japanese cult saying that El Cantare (I'm thinking of a specific group) is the real name of God. Are any Christians going to admit this? No! They call God by the actual name they use.
The word proper Jews use is Elohim which means "God" (but it's the name they use, and when written in Arabic may read "Allah" but importantly it translates to "God"; that the word Allah doesn't translate makes it a name, and more importantly makes it a cult of racial superiority, which is not the way toward any sort of spiritual growth). What Arabic Bibles should do is write the word in Hebrew (
Elohim - Wikipedia ) to remind them that this word is not to be pronounced, or use the Lord (
https://www.wordhippo.com/what-is/the/arabic-word-for-0cb26e2242f1e2f5cbbc8204af141dee67d5fa79.html ) for their text.
As for your second statement, the concept is different. "Allah has no son", and they reject Trinity understanding it as polytheism.
The concept of Trinity doesn't come from thin air though. In Hebrew and Christian scripture, the Trinity is referenced even in the Old Testament, though Jews don't have a formalized Trinity theory.
The Trinity in the Old Testament • Jews for Jesus
The spirit of the Lord walks over the darkness during the creation.
The spirit of the Lord leaves King Saul, and he is possessed by an evil spirit.
Lady Wisdom is God personified (as a just woman). Just as God is personified later in Jesus.
This happens again when a "man" wrestles with Jacob, making him his name Israel (wrestles with God).
This happens still again when God and some angels visit Sodom and Gomorrah.
The Quran has no real equivalent, because it rejects all notions of Trinity. The Jews simply don't have a formalized belief in it. There is a difference between having no theology of something and rejecting belief in something.