I think that it is clear what is meant here, as far as inseparability, whether from a Trinitarian perspective or the Mormon perspective. First, let’s look up “inseparable”:
Webster’s:
1 : incapable of being separated or disjoined
2 : seemingly always together : very intimate
merriam-webster.com/dictionary/inseparable
The Father, Son, and Holy Spirit are inseparable. They are united in purpose, will, and intent (I will leave off substance so we can focus on what we agree on,however it has no effect on my argument). As you said to nancy, they are not three powers, but they are one power. Therefore, within the separatness that we both acknowledge, that they really are separate and distinct Persons, they are also inseparable on another level, the level which makes them One. Inseparable here does not mean that they are attached to each other, which I think is how you take it, but that while they are distinct, they are inseparable on a totally different level. There is a real relationship between the Three, and thus they cannot be separated from each other.
Tertullian actually explains this further in that article:
newadvent.org/fathers/0317.htm
“oikonomia” is actually found in the Bible! “Oikonomia” is Greek for “household management” or “law of the house”, or other related terms. Tertullian defines it as “dispensation”, and this is actually how various versions of the Bible translate it. Ephesians 3, from verse 9 on, is directly related to what Tertullian is speaking of (and clearly calls it a mystery), namely that God was revealed through Jesus Christ. You may be interested in this article:
godseconomy.org/quotes/index.html
Therefore, I still do not see what is internally inconsistent here. The Father, Son, and Holy Spirit are three separate, distinct Persons, yet, they are inseparable as to their will, intent, purpose, power, etc. They are all related to each other, and come together, with the Father as the source. And “oikonomia” is a Biblical term, and is related to the management of things, as we can read in Ephesians 3, for one.