And the very word you want to quote is indeed a scepter a mark of authority. No doubt you would apply the same logic to the parsing of ‘Thy rod and Thy staff they comfort me.” Nice try but....not
The word "shebet" As defined in Strong's Exhaustive Concordance of the Bible defines it in English, and shows the usages in the AV:
shay'-bet
From an unused root probably meaning to branch off; a scion, that is, (literally) a stick (for punishing, writing, fighting, ruling, walking, etc.) or (figuratively) a clan: - X correction, dart, rod, sceptre, staff, tribe.
Young's Analytical Concordance to the Bible gives the usages as: dart, 1; pen,1; rod, 34; sceptre, 10, staff, 2; tribe, 141.
Genesius's Hebrew and Chaldee Lexicon to the Old Testament Scriptures yields six meanings with their related use texts:
1. a staff, stick, rod -- used for beating or striking (Is. 10:15, 14:5); and chastening (Prov. 10:13, 13:24, 22:8
2. a shepherd's rod, a crook (Lev.27:32, Ps. 23:4)
3. the sceptre of a king (Gen. 49:10 etc.)
4. a tribe of the Israelites, so-called from the sceptre of the leader or prince of the tribe (Ex. 28:21, Jud. 21:2) (etc.)
5. a measuring rod (Ps. 74:2, etc.) 6. a spear (2 Sam. 18:14)(dart in AV, lance in DRB)
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The Hebrew word can be interpreted as "sceptre" in English, but not in this context of Prov. 13:24, where a literal interpretation is intended and demanded. The correct English word for this context is "rod" which the translators of AV, ASV, RSV, NASB, DRB, NIV, and others choose. No translator has selected "sceptre" as related to this passage. Your tack of trying to reinterpret this passage as a metaphor of exercising rulership is contrary not only to common sense, but to eminent commentators, of whom Matthew Henry exemplifies:
Proverbs 13:24
Note, 1. To the education of children in that which is good there is necessary a due correction of them for what is amiss; every child of ours is a child of Adam, and therefore has that foolishness bound up in its heart which calls for rebuke, more or less, the rod and reproof which give wisdom. Observe, It is his rod that must be used, the rod of a parent, directed by wisdom and love, and designed for good, not the rod of a servant.
2. It is good to begin betimes with the necessary restraints of children from that which is evil, before vicious habits are confirmed. The branch is easily bent when it is tender.
3. Those really hate their children, though they pretend to be fond of them, that do not keep them under a strict discipline, and by all proper methods, severe ones when gentle ones will not serve, make them sensible of their faults and afraid of offending. They abandon them to their worst enemy, to the most dangerous disease, and therefore hate them. Let this reconcile children to the correction their good parents give them; it is from love, and for their good. (see Heb. 12:7-9)
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What you need to realize is that this passage is literal in interpretation, literal in language, and when the parent needs to use force if necessary to obtain compliance, he is to beat the child with a stick until compliance is obtained. Do you insist that one is to literally beat the child with a king's mace? or to beat him with a tribe of Israel? or with a spear shaft or measuring rod (well, maybe)?
The point is made that the Scripture as interpreted means exactly what The LORD wants the writer to say to you in your language, and not what you seemingly want it to say.
Now, regarding "thy rod and thy staff, they comfort me" -- the rod of the shepherd is used exactly as intended -- to beat the erring sheep back into the way. It is known that an obstinately disobedient lamb is likely to have its leg deliberately broken by the shepherd. The result is that the lamb cannot run away, but will be carried by the shepherd until the leg heals. The lamb will never leave the shepherd again. Sometimes severe methods are needed for oppositional defiance, that it never be allowed to become habitual.
In the figurative-literal sense, God does correct his children by chastening through consequences, illnesses, or other calamities as a rod of correction. In this sense, He may also use His Word as a rod of chastening. The true believer, who errs and is corrected by the the Master through earned consequences permitted by him, finds comfort knowing that the Master's attention is ever on and for the welfare of his children. If you have never received chastening at His hand, then you are not his child. Hebrews 12:8 calls such a one something else.
But in the case of a child, the parent is assigned by God the chore of exercising literal, corporal chastening as needed, and the Scriptural mode is by a literal rod fitted to the child's size and sensitivity. But this needs to start early, much earlier than the atheistic child-behavior theorists want to acknowledge.
The point is made. If you haven't gotten it and admitted it, others will. You cannot mix Dr. Spock and God's Word and come up with a Christian child believer-disciple.