It is just a rule. It cannot be explained. Explanations are just post-facto layman rationalisations; these are not particularly rigorous or useful. Do not waste time looking for reasons for prepositions. You just have to remember them.

"At" implies a direction or destination. In your sentence it could be thought of as "in the direction of": 'She smiled (in the direction of) her husband.' 'She smiled at her husband.' When used as a destination it would be something like this: 'He arrived at work'. At is also used in combination with other words to express a degree of something. Such as: 'He did not understand at all'. Which is like saying He didn't understand anything. or 'She did it at once'. Which is like saying she did it immediately.

We could explain it by saying that "at" makes her husband the direct object (or even target!) of the verb "to smile", which doesn't need an object. However, you just need to learn it as a collocation: smile at, look at, laugh at... It is definitely NOT a phrasal verb.

Because it's a kind of phrasal verb collocation and you always have to use "at" as a preposition with "smile" in this form: smile at somebody/something, the meaning is she is looking "at" her husband and smiling. Please pay attention smile "to" somebody is wrong. Other useful kind of smile noun phrase is: have a smile "on" somebody's face (You have a smile on your face) The best way to learn is you should just memorize them. Good Luck

Some verbs take only a certain preposition after them, you need to remember them, for example, to listen TO, to smile AT, to depend ON/UPON, etc.