The phrase "the acquisition of a special connection with their ancestors" could be grammatically correct, but it may not be the most appropriate collocation to use in this context.
Here, "acquisition" usually refers to the act of obtaining or gaining something. However, when used with "connection," it can sound awkward or even unnatural.
Instead, you could use a different verb-noun collocation that conveys a similar meaning, such as "forging a connection" or "developing a connection" with their ancestors. This would make the sentence sound more natural and better convey the intended meaning.
So a possible alternative sentence could be:
"In conclusion, people's motivation to learn historical facts about their houses can range from the desire to be safe to forging a special connection with their ancestors."