An alternative way to phrase the question is to ask whether a preposition should be repeated after et.
I went through a book for all the examples of et used with prepositions in a way that would allow both options.
I excluded the preposition inter because it would make little sense to say inter Sequanos et inter Helvetios instead of inter Sequanos et Helvetios.
I chose the first book of Caesar's Commentarii de bello Gallico, and I found these:
- 1.5: ab Sequanis et Helvetiis
- 7.4: ab iniuria et maleficio
- 9.4: sine maleficio et iniuria
- 11.1: per angustias et fines
- 13.5: ex calamitate populi Romani et internecione exercitus
- 21.2: cum duabus legionibus et iis ducibus
- 26.1: ad impedimenta et carros
- 34.1: de re publica et summis utriusque rebus
- 37.1: et legati ab Haeduis et a Treveris
- 41.3: cum tribunis militum et primorum ordinum centurionibus
- 47.4: et propter fidem et propter linguae Gallicae scientiam
- 48.2: ex Sequanis et Haeduis
- 53.6: de tanta voluptate et gratulatione
Based on this sample, it seems that the dominant option is not to repeat the preposition — or, in other words, to place et inside a prepositional clause.
There are two exceptions: 37.1 and 47.4.
Both of them use the emphatic et…et instead of a single et.
Caesar's style, at least in this particular book, seems to be to always place et inside a prepositional clause, with the sole exception of using et…et in the sense of "both…and".
Based on this sample, constructions like de Latona et de Niobe without a preceding et are not used.
The sample is way too small to rule out anything like this definitively, but Caesar seems to avoid this.
So, quite opposite to your guess, my little study suggests that your first option is bad style and the second one is good style.
(The adjectives "bad" and "good" are to be taken with a grain of salt.)
If what you suspect to be bad style is indeed bad style, then Caesar has consistently bad style in this respect.
Other authors may have different idiosyncrasies, but at least you are not required to repeat the preposition unless you want special emphasis.