"This will lead to family suspecting their mother of cheating or crime."
Generally not with the proper cover story. Stuff like working as a civilian purchasing agent for the military or other government agency provides an element of truth and can be strongly consistent with the realities of the true job. Travel for purchasing deals vs espionage, etc look the same for the family. Even better is if they actually are involved with the purchasing deals since it makes for a more solid cover.
When I was a kid, there was a guy at our church who had spent some years at a South American embassy and was vaguely in the defense industry. There were little bits of his story that all had us suspecting he likely did cloak and dagger stuff for the CIA in reality, but no point in really asking him for the truth.
Generally not with the proper cover story. Stuff like working as a civilian purchasing agent for the military or other government agency provides an element of truth and can be strongly consistent with the realities of the true job. Travel for purchasing deals vs espionage, etc look the same for the family. Even better is if they actually are involved with the purchasing deals since it makes for a more solid cover.