Hi, Mika. Only the first one "People often have difficulty in returning to their jobs or getting promoted after giving birth and raising their children." is correct.
To add to f6pafd's correct answer, unlike "difficulty," which can be uncountable and take the zero article, the singular noun "disadvantage" will always need a definite or indefinite article or some other determiner, for example:
- People often have the disadvantage of not being able to return to their jobs or (of) not getting promoted after giving birth and raising their children.
Notice that the sentence with "disadvantage" in the opening post is also inconsistent because the disadvantage consists of NOT being able to get back to work or to get promoted. Also, "getting promoted to their (previous/current) positions" does not make sense.
Instead, people find difficulty in getting something positive, which is returning to their jobs and getting promoted (by definition, to a new, higher position).