I don't see anything fatal in the pic. More pics might help, unless what you've shown is the worst of it. Mixtes and step-throughs tend to have a fairly heavy seat tube due to bending loads there. I'd say "ride it and see" unless you're very risk-averse. Even in the worst-case scenario where it breaks, it will still not likely cause a crash, she'll just notice the handling get funny. Probably after a long time of creaking or clicking with each bump or pedal stroke as the crack starts small and slowly propagates. Typically the crack grows to at least halfway around before the rest lets go all at once, so you get lots of notice. Plus the crack (if there ever is one) would be in a very easy place to see.
Mark B