Sounds to me as though the crucial thing is enabling the line manager to deal with this herself, by giving her whatever emotional/practical support you can, but ensuring it's her dealing with it.
From what you say, the basic problem is that some of the team members are not showing (and therefore presumably not feeling) respect for this manager. So it's really really important that consequences of their behaviour come from her, not you. Otherwise it may well make their level of respect for her go down even further. You may find they think 'oh she can't even deal with a bit of grief from us without running to her boss and getting her to deal with it for her', and the bitching behind her back will not stop, it will only become more discreet and therefore more difficult to deal with.
I would see your role as meeting with her regularly, identifying together what actions can be taken to address this problem, (there could be all sorts of things that could be done), then working out together how the plan will be implemented, what the likely developments might be, and what the consequences will be for failure to improve. You need to provide an ear for her to whinge into, practical advice about handling the situation as much as she needs, even the little things if she finds that helpful. But you can and should do all this behind the scenes. That way she will not feel abandoned and unsupported in a difficult situation, as many managers do, but will feel confident of your full backing, will feel more empowered as a result, will know she has someone experienced to bounce ideas off and talk things through with, will gain confidence as she deals with the situation herself, and will hopefully gain the respect of at least the majority of the team in the process.