Judging from a normative grammar oriented, rule-based point of view, this sentence would be considered wrong. The question whether vom is to be considered a contraction (I think it should) or not does not really matter. The OP nails it: the problem is the divergence of the gender of Krieg (m., hence von dem Krieg or vom Krieg) and Sorge (f., hence von der Sorge).
However, in practical use, most native speakers might not even notice. Pragmatically, the focus of attention is limited, and when arriving at Sorge, one might have already forgotten whether there was a vom or von dem in the first part of the sentence. One could interpret this in a way that the vom, even though it is the contraction, is still conceptualized as von dem:
Hier erzählt sie von dem Alltag im Krieg, der Sorge um ihre Familie und dem Stolz der ukrainischen Frauen.
This would be fully correct, and the speaker (writer in this case) might have had this in mind. For the listeners (readers), this will usually be the way they understand the original sentence. Most might not even spot the subtle grammatical inconsistency.
Whether this sentence appears problematic to native German speakers depends very much on who you ask. There is a bunch of people who fancy a very normative approach in grammar. This kind of approach to grammar is also used for social signalling by some. For most people, this inconsistency would be too subtle to even spot it. As it does not affect the meaning or create ambiguity, I guess most people would not be bothered, even if they spotted it.