How do you translate "could have been" sentences? For example, how do you translate this: "All his wife wanted was a peaceful life. When he returned from the war, their lives could have been peaceful, but the government situation at that time prevented it." 

I have no idea how to say these kinds of "could have/would have" hypotheticals in Chinese.
'could have been' basically means “本来可以” while 'would have been' means “本来会”. For example

He could have been there but there was an accident.
他本(来)可以到那里的，但是出了点意外。
He would have been a doctor if he wasn't hurt.
如果他没受伤，他本会成为一名医生。

Generally, hypotheses in Chinese include the character “本”, like “本来”, “本会”,“本能够”,“本应该”,“本可以”,“本可能”.
Well, there are several mistakes in Kevman's translation.

“妻子”


All his wife wanted was a peaceful life.

This should be

他的妻子只想要平静的生活。

'All his wife wanted' means “他的妻子只想要” rather than “他的妻子们”

“他们”


their lives could have been peaceful

This should be

他们本可以平静地生活着

'their' means “他们的”, because it refers to the man and his wife.
When it refers to people including male and female, it should be translated into “他们的”. Work the same for 'they', 'them' and 'themselves'.
The rest is just as Kevman said.
---------------divide-----------
For Kevman's translation is not shown, I will type the whole translation below.

All his wife wanted was a peaceful life. When he returned from the war, their lives could have been peaceful, but the government situation at that time prevented it.
他的妻子只希望过平静的生活。(但)在他从战场归来后，繁忙的政府公务没让他们过上本(来)该有的平静生活。

This translation is more natural but not formally same. That's why you see “本该有” rather than “本可以”。
One more thing, just as Jesse said, there is a precondition that if everything was like before.