TheIt is unambiguous that the wife is the one who would be doing the warning in this case, and this sentence is being spoken to her, by the boss, who is directly asking her to caution her husband.
The function of から is really very similar to "from" in English, as in going from point A to point B, last from time A to time B, being made from something, and others, but especially in this case, hearing something from someone. Therefore the usage of から in this case basically mirrors the English meaning: the boss wants the husband to hear it from the wife. It might be slightly confusing because we don't use "from" as a command like that in English. Like you can't say "Please caution your husband from yourself."
The grammar of から in this case might be debatable, though. The following is my original interpretation, with amendments later:
I admit I am kind of speculating here, but my assumption is that から is not playing the exact role of が. When you make commands there is an implied subject, so even though you don't include the subject marker in (~が)~してください, it is understood. The 奥様から in this case is emphasizing that he wants the wife to caution the husband herself, but since there's no が and he's explicitly saying 奥さまから, it kind of sounds like から is replacing が.
Another way to say it might be (奥さまが)自分から注意してください。 I don't know about you, but to me it feels a little more obvious that way, and the separation of the subject version of 奥さま and the origin-of-action version of 奥さま is shown.
EDIT:
The discussion in the comments has led to the suggestion that から may in fact be able to mark the subject. If this is true then 奥さまが自分から注意してください is technically different. If we permit から to be a subject marker then the sentence can be interpreted as is: 奥さま(から・が)注意してください。