What Army regulation covers me being forced to use my POV to transport other soldiers for Army duties? Am I required to do it?

There is no such Reg, and certainly no local policy requiring such.
Id guess this is an SM that lives near you that has no legal mode of transport and has cited that as to why they cannot get to the required place of duty on time or at all.. the COC is thinking "Well heck, Isom lives right next door, SPC Dingleberry can ride with him.

I was taught by a Senor NCO I much respected, unless it's illegal or immoral, don't say no,,,, Instade let the leader know what it will take to make it a yes.

My solution to the scenario I made up and laid out above?
"Marqueze, need to give SPC Dingleberry a ride into PT in the morning and home after the last formation"
"Ok 1SG I can do that"
"Dingleberry, meet me at my car in the morning, I'll be leaving for PT at 03:30, Text him the same info"
At 03:30:01 depart for work.
"Marquez, where is Dingleberry?"
"He did not show up for the ride"
12 hours later
"Marquez give Dingleberry a ride home"
"Ok 1SG"
"Marquez, why are we going this way....Away from our apartment complex? "
"Oh, Im going to a laundry mat in the next town over, doing 2 weeks of laundry, and washing all my TA-50...Oh by the way, I am leaving for PT at 03:15 in the morning, be there if you want a ride"

Ride-sharing will be terminated by Dingleberry or the COC soon enough......And if I was your 1SG, I'd not even be mad at ya.

You will probably want to get verification on this (Legal Assistance Office, IG, etc.), but I think you're on solid ground, although a reasonable argument can be made to "pick and choose your battles". This assumes that you're not leaving out pertinent details on your situation.

Look at AR 58-1, "Management, Acquisition, and Use of Motor Vehicles", dated 2020.

From the reg:

Summary: "This regulation prescribes Department of the Army policies, responsibilities, and procedures for the management, acquisition, and use of Army-owned, Army-leased, or otherwise controlled non-tactical vehicles. It implements DODM 4500.36 and DODI 4500.36."

Your command can argue that your POV is not an "Army-owned, Army-leased, or otherwise
controlled non-tactical vehicle", so the regulation does not apply to your situation. Read into the regulation and you'll find a great nugget that supports your position.

Applicability: "This regulation applies to the Regular Army, the Army National Guard/Army National Guard of the United States, and the U.S. Army Reserve, unless otherwise stated. Also, it applies to all Department of the Army Civilian employees, foreign nationals, and contractors employed by Department of the Army."

I don't know your status, but this rules out any command argument that "the reg doesn't apply to us". It applies to AD, USAR, and NG.

From Chapter 2-1:
"b. When allocating resources for transportation missions, planning begins with a determination that motor vehicle transportation is essential for the performance of an official mission. When such a determination is made, the following methods will be considered in the order shown, subject to their availability and capability to meet the mission:
(1) Scheduled Government bus transportation service.
(2) Specially scheduled Government-leased or Government-owned bus transportation.
(3) Government-owned or Government-leased NTVs.
(4) Voluntary use of privately-owned vehicle (POV) on a reimbursable basis.
(5) Taxicab on a reimbursable basis."

In the absence of guidance that they can require you to use your POV to transport other soldiers for a valid mission requirement, this reg indicates that you must have volunteered to use your POV, and that you must be reimbursed.

Also, there's a fiscal law argument against this because using your POV for free (assuming no reimbursement) is an in-kind donation to your unit, and that is against the law (it's called "supplementing an appropriation"). This is a very minor violation of the law, but it still may very well be considered a violation. For example, a billionaire can't donate money to build a new military hospital in support of an installation's healthcare mission. Congress considers that a violation of appropriation law because if they wanted you to have a new hospital, they would have appropriated money for a new hospital. The absence of the appropriated money means they do not authorize a new hospital. At a much lower level, the same thing goes if your command tells you to use your personal funds to buy fuel for a military HMMWV ("supplementing an appropriation"). Likewise, a troop can't make an in-kind donation in support of an operational mission, such as being required to use your POV (compensated or otherwise). The amounts are all very different, but they are still violations.

Again, verify this, but this reg seems to support your position.

Even if there is a regulation, it's likely an obscure legal/ethical federal policy and it won't do you any good to cite it. It will likely cause eye rolls.

That being said, your local legal team or even the IG will back you if you wanted to push the issue. I've seen it before, Soldiers not wanting to use their POV for something. It's perfectly fine, that's your right. So, if you're sure about this, just bring it up in discussion through your chain of command.

However, do it as a team player. Offer alternatives to the situation. Protecting yourself in this isn't about throwing the book back in the face of your leadership, it's about standing up for yourself while also displaying commitment to the success of others and the willingness to serve.

Remember, this job requires sacrifice. Sometimes that means running into a hail of gunfire to pull someone off the X, and sometimes that means waking up early on our own time to drive someone with our own vehicle to CQ, that is miles away.