So instead of thinking PO kidnapped them, the Dragons immediately thought The Moon Sisters betrayed them ? Were the Dragons that stupid ?

They weren't wrong tho

i think it was cuz the moon sisters did not join Nibelung in the war of funerary flame

Yes

While plagued by Forbidden Knowledge, Apep was far more vitriolic and irrational than she became after it was purged from her, so it's possible that Nibelung's behaviour had been warped as well.

They willingly worked with the HP. But, I mean, it was mostly at gunpoint. And the HP offered protection against the abyss, and Nibelung left to get some milk, so it was the most logical decision for pacifists to make.

They also didn't join in on the 40 year war or the year of funerary flame.

But they hosted Koitar and the Voyager at their palace for their catfish wedding, so they *were* willing to take a side against the HP. Just not the dragons' side.

From the dragons' POV the Moon Sisters did betray them.

When you see the people whom your leader left in charge do nothing, keep silent and are seen cooperating with the enemy while you and your people are being genocide by said invading force. You are going to think they betrayed you even if that wasn't the case. So no they aren't stupid they just didn't have full picture. 

Weren't they supposed to take care of things while Nibelung was gone? Then they didn't even try and the dragon were left to defend themselves?

Nibelung was not corrupted by the abyss at this time ?

Can't judge. I have no idea accurately how is the situation and circumstances at the time when PO and Dragons and Nibelung at war. The game said the moons "can be used as weapons". That's quite technical, means probably the subject moon goddesses are using the physical moons but they are not a united entities to the physical moons. The moons could be really some kind "sci-fi weapons".

It is the dragons who say that they betrayed them because the goddesses of the Moon refused to answer their question about the return of Nibelung (see Ineffa's weapon). They even attempted to recreate new moons to replace them.

HP didn't kidnap them, he ignored them because they posed no threat to him and only wanted to protect Teyvat.

They were neutral, but Nibelung, corrupted by the Abyss, took this as betrayal and ended up turning them into weapons that destroyed all life on Teyvat. The Moons didn't agree with this, but being imprisoned, they had little choice.

Two of the Moon goddesses decided to join Nibelung, and the last one remained neutral.

The two who joined Nibelung (in Nicole's explanation, she says that the majority joined and one remained neutral) were certainly the moons that were destroyed by HP, while Frostmoon was simply excluded from Teyvat, waiting for the day when she could return.

The Moon Sisters realised they were not powerful enough to fight back against the Priomordial One so they chose to surrender. They realised a war would harm Teyvat and their primary objective was to protect Teyvat.

When Nibelung returned, corrupted with forbidden knowledge. He saw the Moon's were working with the Primordial One and got angry. He took control of the three moons converting them into weapons to use in his war against PO, while imprisoning the Moon Sisters. PO saw the moons under Nibelung's control and assumed the Moon Sisters betrated them and destroyed one of the moon, sent the Frost Moon out of orbit of Teyvat and the Crimson Moon sunk into the ocean.

The Moon Sisters took the best course of action as they were not powerful enough to face PO. But in the end both Nibelung and PO believed the sisters betrayed them and ultimately they were forgotten and died in their imprisonment.

The dragons believed what their King, Nibelung told them that the moons betrayed them.