Hello, Aracan! Welcome to the forum.
I think it should be pointed out that trying to compare English grammar to German grammar (or any other language's grammar for that matter) is not the way to go when trying to understand the intricacies of English. While it is fascinating to compare how English works with other languages—and the very reason I got interested in linguistics in the first place by the way—it may make you fall into the false belief that you know how English works because you're putting an equal sign between a grammatical structure used in English and a grammatical structure you already know from German, which may or may not correspond to each other exactly.
I agree with 5jj. Textbooks and many English teachers recommend using the past perfect far more often than it is actually used on a daily basis by regular everyday native speakers. I think their point is that they want to teach you when using the past perfect is possible, but they accidentally make it seem like they're telling you that it's mandatory to use that structure in these contexts. From my own experience—for what little it's worth—the past perfect is used far less than textbooks make it seem it actually is. If the sequence of events is already obvious from the context, or words that clearly signal what the sequence is are used, the past perfect is not necessary and can be freely replaced with a non-perfect past tense.
"In 1990, Tina lost her job and so she began looking for work in London" looks like something I'd expect to hear from a native speaker. I might even argue it would be more common to hear that than "...Tina had lost...", but that's not the point of the exercise your daughter was given. The point is that she should understand when the past perfect can be used, and that in such exercises she should use it whenever it's possible, even if it's not strictly necessary. It's very difficult to make exercises where the past perfect must be used instead of the past simple, indisputably, so they usually just give those where it can be used.
While it's tempting to disagree with your English teacher, it's advisable to try and understand the reasons behind their choices and comply with their requests. They're usually on to something after all. ;-)