"Mis padres y yo nunca nos hemos gustado."
Traducción:My parents and I have never liked each other.
It's not actually incorrect to put the "never" first. (At least, not in US English.) However, it's much less common, and it changes the emphasis. "My parents and I have never liked each other" is a simple statement of fact. "My parents and I never have liked each other" is pronounced with a strong emphasis on the "have," and it's the sort of thing I'd say if my parents and I had just argued AGAIN, after a lifetime of not liking each other. (Similarly, "I have never done that" is a simple statement of fact, but "I never have done that" implies that I've always wanted to do it, or that you would have expected me to.)
In this sentence, the primary translation is correct, but I'd say that "never have" should be accepted as an alternate translation. If you report it, they'll add it to the database.
The rules given at that link are more stylistic than grammatical. They're alright as guidelines for clean writing, but they're oversimplified, and good usage can depend a lot on the adverb and the sentence. For instance: the statement "an adverb modifying a two-word compound verb comes between the helping verb and the main verb" is a fairly reliable way to construct a good sentence, but it's not the only way, and sometimes, it's not even the BEST way. "They had rapidly returned" (with the adverb in the middle) is no more correct than "they had returned rapidly" (with the adverb at the end): changing the adverb placement changes the tone of the sentence, but neither version is ungrammatical. "She had come quickly" is fine and completely correct, whereas "she had quickly come" sounds a little awkward, like it's missing a destination. "I have never gone there" is neutral, whereas "I never have gone there" implies something like whistfulness (as though I keep meaning to go, but never do). And "you should usually put the adverb in the middle" is neutral, whereas "you usually should put the adverb in the middle" places extra emphasis on the "usually," as though I want to make clear that it's USUALLY, but not ALWAYS.
On the whole, English rules about adverbs are more flexible and less predictable than grammar.com would like to think. This is a completely different situation from "if I was a girl...," which uses the wrong verb form (simple past instead of that weird subjunctive that English has, that's ALMOST the same as the past tense, but not QUITE), and in doing so, breaks a hard-and-fast grammar rule. (The English language is much fussier about its verb tenses than its adverb placement, apparently. =) )