I'm sorry that you have this frustration. There is nothing worse than working your butt off and not feeling that you are being supported in your work. And FYI - most admin/management teams at most jobs are screwed up - this is nothing new. It is what happens when money and not people are the bottom line.
Reading your post I can say that I do not approve of the response that was given by this charge nurse when asked for help, nor do I approve of doing chart audits instead of providing support for the patients. But, having been in the same situation - management having to work as staff, I also know things that staff persons don't know, that can contribute to the problem you are concerned about.
As management, you have a job description that says you have 100+ tasks you must perform in order to keep your job. This is in addition to working as staff. When you work as staff you are generally unable to get your managment duties completed. You then are yelled at by admin for not completing those duties and they don't care that you had to work as staff all week, they just want the numerous reports completed and meeting attended. When you work as staff, this also takes away the time that the poor manager/supervisor has to work on fixing the problems of the unit so that the staff are happier, the patients are well cared for and the hospital looks good. So the vicious cycle continues with unhappy patients, unhappy staff, unhappy administrators and the manager is caught in the middle and never seems to be able to effect any change to make things better. The manager is merely used as a stop-gap for lack of staff and the scape goat of both staff and admin when things aren't perfect.
My guess is that this is the kind of situation that your coordinator is in. Sometimes the coordinator has to let the staff "struggle" on their own in order to get the management job done because admin is threatening them. It isn't right, it isn't fair, but it frequently happens. I don't agree with refusing to leave the desk because there won't be anyone to answer the phone, but it may be that the CNO has just chewed the coordinator's butt about poor customer service and insisted that the phone be answered by the second ring and this coordinator has not been able to find a better solution to this problem.
It could also be that she has not been given education on being a charge nurse, much less a coordinator. Not everyone is a born leader. There are people who can be put into a leadership position and know just how to balance the different responsibilities they have to make at least half the people happy most of the time. But most people in leadership positions do not have this ability. They may be able to prioritize patient care but when it comes to supervising, they have no idea what should be a priority. They get so focussed on performing the tasks that admin has given them that they are unable to see the big picture and know what the staff's needs are. I have only worked for one hospital that held education classes for new charge nurses as well as new managers. But that was also the best hospital I ever worked for. They knew that education is the key to getting good results. Unfortunately education is one of the first budgets to get the hatchet when fiscal year comes to an end and money is tight. And that is yet another vicious circle that most admininstrations don't get - keep education, get better trained staff, have better patient outcomes, have happy patients, get more patient business etc.
Or it could be that she is just one of those lazy nurses who are there to pick up a paycheck. I hope that is not the case but there are nurses out there that truly don't want to work and will do as little as possible to get by.
So, you have 3 theories as to why this nurse has done these things. I hope that she is just needing education or has not yet been able to figure out which things to fight admin on in order be able to give the staff support (like refusing to do chart audits when direct patient care is more important). The worst thing to do is to go tattle. If you are being directly targeted by a supervisor and must defend yourself or a patient is in danger, then go to their supervisor. If you are not protecting yourself (physically or career-wise) or a patient, then it will look like you are tattling because you just don't like the woman. Especially if it is common knowledge that you have made gossipy comments about her to other people.
My suggestion would be to keep a log of all these instances where you find there is a problem - date, time, circumstances, names of people involved. This gives you objective data to work with. Try talking to this woman. Don't accuse her of being lazy or a bad boss. Tell her "I felt really bad the other day when you were unable to come help lift that patient. I felt that I needed you and you were unavailable because you had to stay at the desk and answer the phones." Make it seem like YOU are the one with the problem and that she hasn't done anything wrong. This is much more likely to get her talking to you because she is not being threatened. You might actually find out why she did what she did. DO NOT discuss this with coworkers. The fastest way to get your supervisor to either hate you or be even more "useless" is to gossip with others. Go home and rant at your husband/mother/best friend who doesn't work with you/pastor/dog, but avoid badmouthing this woman at work. It ALWAYS gets back to them because women are notorious for letting things slip. And this woman will not want to speak with you if she knows that anytime she says anything to you, the rest of the staff will hear and the message usually gets distorted along the way. If she expresses a need for assistance in doing her job and you might be able to help - then offer your help. If you can't physically help, offer her emotional support in doing her job. Yes, you are the one that really is needing the support, but if you support her she will more likely be aware of needing to support you as well.
If you feel you must go to her supervisor. Don't accuse her of laziness, not doing her job, etc. Unless you have seen a copy of her job description and latest evaluation you don't really know what her job is. Simply go to the manager with your concerns that the you are not getting the support you need - and be specific. You need specific instances where you needed help and you didn't get it. Suggest to the manager that you have noticed what a difficult time that the coordinator is having trying to be a staff but also get her management responsibilities done. Offer solutions. Everyone has something about their job that they hate and they all want to complain. If you want your manager to take your concerns seriously, you have some solutions to offer. Your concerns may get to the top of the list because then the manager doesn't have to come up with possible solutions all on her own. It doesn't matter if your solutions won't work, but it does look good that you have actually thought things through, looked at the rationale behind what is going on, identified the problem, and found some possible ways to fix things. Sounds a little like the nursing process doesn't it?
Remember, you may not see any immediate results from your hard work with this. You may not see any visible results at all. But there is so much that goes on behind the scenes that is not always appropriate to share things with the staff. And if she really is lazy and got in trouble for it - do you really think that you are going to find out about this?
In these days of healthcare, things are going to suck. And there are always going to be people who are your supervisors that don't live up to your expectations. You have to decide how to handle it. If you want to change things you have to start with YOU. If the charge nurse isn't helping people, then you need to step up and start acting as more of a resource person. Someone will notice. It may not be the boss but if the rest of the staff are happier because they know that they can come to you for help and you dont' gripe and moan, then you will have made yourself happiers as well - because the staff have less to gripe about because they are happy with you.
And if you truly can't stand it - consider getting out of nursing. The grass is never greener anywhere else. The only difference is the type of manure you encounter in the pasture and which smell you can tolerate.
Good luck on trying to find a solution to this frustrating problem. This problem is not new and definitely is not limited to your unit.