"she's not getting to see our boys as much as she'd like due to the hours she's working."
It might not actually be about this. Maybe she is feeling run down, or taken for granted by her family or work collegues? Maybe there is some problem at work and she does not like to say what, so was leading up to it indirectly by indicating she would rather be somewhere else other than work? Does she do shifts and she is finding it disruptive – some people never manage to cope with the physical aspects of working odd hours.
I think perhaps she wanted you to ask what is wrong, because at least that would show care and concern. I am not saying either of you is right or wrong, just that there is likely to be a lot more to it than how many hours she spends with the kids. Does she have a friend or family member you can ask for info from? If she is bursting into tears and then getting either sulky or angry, there is clearly, to her at least, a deep felt and significant issue here. You need to sort it, as this sort of thing is how breakups start – one member of the partnership not feeling 'understood' and both failing to communicate sucessfully about what is going wrong, or worse, pretending nothing is going wrong until it is way too late to fix.
