The Berserker Axe is a +1 axe that increases max HP by 1 HP per level, but has a curse, part of which states:
Whenever a hostile creature damages you while the axe is in your possession, you must succeed on a DC 15 Wisdom saving throw or go berserk. While berserk, you must use your action each round to attack the creature nearest to you with the axe. If you can make extra attacks as part of the Attack action, you use those extra attacks, moving to attack the next nearest creature after you fell your current target. If you have multiple possible targets, you attack one at random. You are berserk until you start your turn with no creatures within 60 feet of you that you can see or hear.
In my game, the Berserker Axe curse triggered on a player character, and her fellow party members tried using calm emotions, dispel magic, and suggestion ("Stand Down") to stop the curse.
How do each of these spells interact with the curse?
Calm emotions says:
Alternatively, you can make a target indifferent about creatures of your choice that it is hostile toward. This indifference ends if the target is attacked or harmed by a spell or if it witnesses any of its friends being harmed. When the spell ends, the creature becomes hostile again, unless the GM rules otherwise.
You suggest a course of activity (limited to a sentence or two) and magically influence a creature you can see within range that can hear and understand you. [...] The suggestion must be worded in such a manner as to make the course of action sound reasonable. [...] On a failed save, it purses the course of action you described to the best of its ability.
Dispel magic says:
Choose one creature, object, or magical effect within range. Any spell of 3rd level or lower on the target ends.
I ruled that calm emotions had no effect. Dispel magic was cast at the player, not the axe, so no effect, but I'm not sure if it has an effect even if cast at the axe.
Suggestion had me stumped. I had it give the target a 2nd saving throw against the berserker curse.
Were my rulings correct? How should these spells have interacted with the Berserker Axe's curse?
(There are similar questions about competing charm effects, but I'm not sure this is quite the same.)