Lola, management is not omnipresent and omnipotent. They can set the rules but it still depends on the individual staff to comply in good faith and have some give and take. If pt-ers don't pull their pro-rata weight, the ft-ers who care about the outcome pick up the slack unless they also boycott in which case the whole company suffers.
They don't have to be omnipresent or omnipotent.
They do have to manage their team in a way that is effective because that's their job and it's what they are paid to do.
In the PP situation, based on what they say:
Some staff (mainly full time) are being pushed into doing lots of overtime
Some staff (mainly full time) are being stuck with tasks that take them repeatedly over their hours
Some staff (mainly part time) are able to get all the easier tasks
Some staff (part time) are apparently able to get easier tasks by 'crying and whining' (though given that posters evident contempt for her part time colleagues that could easily mean they have stood their ground that they can't do X because they finish at 2.30 and have to pick their children up, which is entirely their right).
The team apparently manages their workload between themselves though based on PP the team clearly isn't managing otherwise they'd not be in this situation. The PP seems to think this is grounds for being pissed off at part time staff though.
So either:
A) Management haven't a clue what is going on in their team, in which case they need to do a better job and be in the loop a bit more
Or
B) Management do know what is going on and they are entirely accepting the current situation, in which case they are ineffective because there's people like the PP who are understandably annoyed at having to always pick up the slack.
Or
C) It's not as bad as PP suggests and they simply have a bee in their bonnet about how they think part time staff don't pull their weight
The PP said she spoke to management about the situation and they didn't care and told her she should go part time if it's an issue. It's a terrible and dismissive response.
So, assuming everything they say is true (and there's no reason to doubt it),it absolutely IS a management issue.
I don't see why PP is directing her anger at part time colleagues for not working beyond their hours because it 'isn't fair' that she does, when the whole situation is a systemic management failure.