I think we can also translate it as "They were having everything they wanted", no?
Your proposed translation isn't great. "have" is used very rarely in the progressive form. This is because it's one of a few verbs that has a strong stative quality, i.e. it describes a state rather than an action. The exceptions are when have does not imply possession such as have a shower, have a meal, have a baby etc. So e.g. if the sentence was referring to eating out then your version would be okay.