Should an engineer design a floor plan for a domestic worker's room next to the owner's bedroom, based on the latter's request, or should he refuse out of fear of misjudgment or potential problems?

There is no harm in designing the room in the desired location. The intention may be good, such as protecting it from unwanted entry. The default assumption is to interpret a Muslim's actions favorably. Therefore, it is impermissible to harbor ill suspicions without clear evidence, due to the Almighty's saying: "O you who have believed, avoid much [negative] assumption. Indeed, some assumption is sin," and due to the Prophet's (peace be upon him) saying: "Beware of suspicion, for suspicion is the falsest of speech."