Well it isn't going to parse that! Two options I can see, that would make more sense than what you have
<chapter>
<verse>Eva said, <quote speaker="Eva">I'm not the one who's underestimating her cleverness.</quote></verse>
<verse><quote speaker="Eva">Or maybe it's you I'm underestimating. Have you finally joined her side, sister?</quote></verse>
</chapter>
Oh and I'd say that the comma after Eva said, is redundant
or
<voice speaker = default/>
<chapter>
<verse>Eva said, <voice speaker="Eva"/>I'm not the one who's underestimating her cleverness.</verse>
<verse>Or maybe it's you I'm underestimating. Have you finally joined her side, sister?<voice speaker = default /></verse>
</chapter>