Valentinian himself seems to have exercised no real authority, and was a figurehead for various powerful interests: his mother, his co-emperors, and powerful generals.
He was thoroughly dominated by the Frankish general Arbogast. When Valentinian formally dismissed Arbogast, the latter ignored the order, publicly tearing it up and arguing that Valentinian had not appointed him in the first place.
On 15 May 392, Valentinian was found hanged in his residence in Vienne. Arbogast maintained that the emperor’s death was suicide. Unlikely.

Reverse: SALVS REI-PVBLICAE, Victory walking left, trophy on shoulder, dragging captive behind her. Cross in left field?
Die Orientation: 6 H
Weight: 1 g
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Reverse: VICTORIA AVGG, Valentinian II and Theodosius seated facing on throne, holding globe between them; palm between legs, figure of Victory with wings spread above; T-R across fields, COM in exergue
Die Orientation: 1 H
Weight: 4.45 g

Reverse: CONCORDIA AVGGG, Constantinopolis seated w. globe & spear
Die Orientation: 0 H
Weight: 0 g

Reverse: VOT / X / MVLT / XX within wreath; ???
Die Orientation: -
Weight: 1.55 g

Reverse: VOT / X / MVLT / XX within wreath; TES
Die Orientation: -
Weight: 0.87 g

Reverse: Roma seated on cuirass left, holding Victory on globe and spear; VRBS__ROMA / Θ */Φ / ANTB
Die Orientation: -
Weight: 1.9 g

Reverse: Roma seated facing, head left, wearing helmet, holding globe and spear; CONCOR_DIA AVGGG / SMNB
Die Orientation: -
Weight: 3 g