poor performing employee

I am currently the senior person in my team, and the youngest, our "admin support" is the most junior member of team and the oldest. Whilst I am not the manager of the team I deputise when he is off, I am also responsible at all times for monitoring the work states and prioritising the work within the team.
The admin support lady has been employed by the company for approximately 15 years, and is a big believer of time served = ability, unfortunately she is incompetent at the majority of tasks that she is allocated, requiring these to be corrected - this normally takes me longer to correct than it would have taken if i had completed this myself - she will not correct her own work as she doesnt recognise that she has made a mistake and does not allow people to feedback to herself.
The management team recognise that she is incompetent but do not have the capabilities to tackle this with her, she is very difficult individual who takes any form of feedback as personal attack on herself - it is always greeted with the response - "ive been here 15 years, you've only been here 3 i think i would know how to do it better than you" - unfortunately she doesnt.
she also has issues taking any direction from myself as she has issues with any woman having more authority than herself.
She has now taken to shouting at me in the middle of the office when she does not like how i decide to manage the work creating a scene and making it a very difficult situation. she only does this when our direct line manager is out of the office - i have complained to management each time she does this, highlighting where it breaches the company harrassment policy.
I have requested that the matter (her manner and incompetence) be addressed as this only creates more work for me - i currently work 10 hour days (contracted 7) as I am correcting her work. the management team are concerned that she is a "nervous breakdown waiting to happen" so won't raise it with her.
the company would save money if she was off sick as her mistakes have cost us vast amounts of money in the past year.
I dont know what else I can do to get the matter resolved - any ideas would be much appreciated.
Thanks, HLB