Why did Darth Sidious hate Darth Vader

Did Palpatine draw strength from hatred or suffering?

"The Force gives a Jedi his strength. It is an energy field that is generated by all living things. It surrounds us and penetrates us; it binds the galaxy together." - Obi Wan Kenobi

That's the first thing to understand. Emotions are not the fuel that drives power. The poweris the force. Traumatic events do not create batteries of power that individuals can later fall back on.

So your question is based on a flawed premise. "Are there examples of Palpatine being angry or experiencing suffering and using these powers to his advantage?" Yes ... but not as you think.

"Anger and pain are natural and part of growth. They give you focus. They make you strong." - Darth Vader

Let's talk about the Sith. The Sith focused on anger, fear, and pain in order to gain power from power. They followed a philosophy that encouraged the strong to rule over or even destroy the weak.

The term "Sith" is generally used synonymously with "The Dark Side". People who used the dark side drew their strength from darker emotions. However, this does not mean that the darker emotions were the source of the power, just the channel through which the individual wanted to focus his power.

So think about it, you can be the calmest person in the world and shake off provocations, or you can get upset about the smallest thing and beat people up to achieve your goals. Both your goals and your methods depend on what type of person you are. The Jedi (or users on the light side in general) used the first path and the Sith (or users on the dark side) used the second.

And here we get to the heart of your question: Sidious never seems to be angry (or to suffer / hate as you put it). A calm man can hit just as hard as an angry man. The power Sidious used was channeled through his hatred of the Jedi, although he never disclosed that hatred to an outside observer.

If you'd like to see specific examples of the next, let's see Sidious display the "expected attributes" of the dark side. I think the end of Episode III will be the next one you'll get. But also remember that one does not have to manifest the extreme state in order to be in power. The emotion is simply the channel or focus.

I would also like to point out that dark side users didn't have to resort to their own emotions. They could also use the suffering and pain they caused or the hatred of their enemy to their advantage. In my opinion, this is where the misunderstanding comes from that emotion is force caused .