1 on the interior wall between the heated and unheated portion of the basement i would not use with a vapor barrier.
Vapor barrier concrete basement walls.
The other option is to set the 2 4 wall framing in 4 from the masonry or concrete basement walls and use just the vapor barrier on the insulation facing toward the living space.
Not to be confused with a vapor barrier which is placed on the warm side of the wall just in front of the insulation and behind the drywall a moisture barrier goes against the basement wall.
If you have a framed wall that is adjacent to a concrete foundation wall where the vapor barrier is next to the drywall in front of the studs the fiberglass insulation gets wet and becomes a breeding ground for mold.
In winter the dew point of the interior air is typically about 50 f assuming an air temperature of 70 f and a relative humidity of 50.
The builder insulated the upper 4ft of the basement wall with a pink batt style insulation which is held to the wall with a vapor barrier.
When the mold grows it will spread to.
Very hot and humid climates may benefit from an exterior vapor barrier that keeps outside humidity from penetrating into walls.
Below grade walls and floor slabs transmit ground moisture through concrete walls or slabs.
Also be sure to use treated lumber for the bottom plate on the wall framing.
The construction of the wall for instance is vital to the use of a vapor barrier.