What are the procedures for a Commander's Inquiry against a Platoon Leader accused of fraternization?

JAG, Lieutenant. That is where you need to go. Not here. JAG.

2LT Hiro Nakagawa "What are the procedures for a Commander's Inquiry against a Platoon Leader accused of fraternization?"
As your question is answered in detail in ,AR 15-6, Chapter 4, para 4-3
"4–3. Procedure
The inquiry will be accomplished in accordance with guidance and direction provided by the appointing authority. The findings of the inquiry should be documented in writing (see fig 4–1 below), and it is advisable to preserve any evidence gathered.

In effect, the CDR sets forth what is to be investigated, the who, what, when, where. The CDR does that themself or assigned another who is authorized under para 2-3
"2–3. Who may be appointed
a. IOs and board members will be those persons who, in the opinion of the appointing authority, are best qualified for the duty by reason of their education, training, experience, length of service, demonstrated sound judgment and temperament. IOs and board members must be impartial, unbiased, objective, and have the ability to complete the investigation in a timely manner. If an appointing authority determines that a person with the required experience and expertise is not available within his or her organization, he or she may request assistance from a superior in his or her chain of command or supervision, or coordinate with a counterpart to obtain an IO or board member with the required
education, training, experience, and expertise to conduct the investigation or board.
b. Except as provided in subparagraph e, below, only commissioned officers, warrant officers, and Department of the Army civilian employees permanently assigned to a position graded as GS–11 or above (or their equivalent, such as a civilian faculty member of a comparable grade appointed under the provisions of Title 10, United States Code) may be appointed as IOs. Non-commissioned officers in the grade of E–7 or above may be appointed as IOs when the appointing authority determines that military exigencies exist and no commissioned officers, warrant officers, or qualified Department of the Army civilian employees are readily available. Voting members of boards may be commissioned officers, warrant officers, non-commissioned officers in the rank of E–7 or above, or Department of the
Army civilian employees permanently assigned to a position graded as GS–11 or above (or their equivalent)"

Preliminary Inquiries https://armypubs.army.mil/epubs/DR_pubs/DR_a/pdf/web/r15_6.pdf

Id ask, what is your question in reference to what is specified in the published procedures, vice what your perception is that differed, is lacking, is not aligned to the AR specified procedures?

Those are the specific questions you need to ask JAG,
The Reg states XYZ, the CDR has tasked SSG Smith to investigate ..is that allowed under the regulation?

The Reg states XYZ, the CDR called the platoon into the orderly room, stated he knew I was guilty and wanted their statements about my guilt" is that allowed under the regulation?

The reg states XYZ the IO tasked must be " IOs and board members must be impartial, unbiased, objective" The CDR tasked my former PL, who was relieved of his duty position when I found him drunk on duty, asleep in a HMMWV in the field.. is that allowed under the regulation?

Research, consider if the CDR's actions are within the authority, in line with regulations, if not, cite the reg, the issue and ask for Jags opinion.

Any commander wanting to stay a commander has already done what the reg requires

"para 4–4. Legal consultation
Commanders and preliminary inquiry appointing authorities must consult with their legal advisor prior to conducting a preliminary inquiry "

As such, its possible the CDR is not following regulatory procedures, but not likely.

Sir, I would suggest by starting with JAG. I think that would be your first course of action. I think they might have the answers you are looking for.