IvanM

Speak to a good agent to map out a possible path. Even then there are no guarantees as the skills in demand change.

Bermudashorts

If your occupation is not on the lists (SOl or ENSOL) then you will not get PR. Not everybody is eligible for PR.

I have no idea what a Global Mobility Manager is or by what other name it could go by, have you cheecked the SOL and ENSOL for something similar even if it goes by a different name.

In view of the uncertainty around this, I would definitely recommend professional assistance before you pull teenagers out of school to have to re-enter in the UK in a few years perhaps.

Seek out your own professional assistance, remember any agent that your company provides is working to get you a visa to help the company but may not have your best interests at heart.

JAJ

If the move is intended to be permanent ...

The safest way to manage a situation like this is to forget the 457 entirely, and do an offshore ENS migration application. That way, you arrive in Australia as a permanent resident on Day One.

If the company says no to this, OR if you're not eligible for ENS, that may require some serious consideration as to whether or not you wish to accept the job offer.

paddyo

Global Mobility Manager is obviously part of the HR team, but not on the ENS list.
You will NOT get a GOOD 4 bed house for $600 in a GOOD suburb, but you might get a DECENT house in a DECENT suburb.
The school issue and whether you move is your choice but as your children are not in the UK system now then to me its a non issue, but, the MOVING will be an issue for the older children as it is very difficult for older kids to mould with other peers who have developed their friendships over years. It can seriously affect them but if they are happy to do so then that will help.
$4500 per annum per child, but only in NSW in public schools. Asking people for what school their kids go to is really a bad idea, that is personal and some people are tetchy about revealing those details to strangers.
Your husband CAN work while you are on a 457, but, some employers will baulk at a long term role as he will be Temporary and not under their control.
Moving from 457 to PR is easy if your employer sponsors you, but if your skill is not on the list of required roles then individual application will be difficult.
Areas to live, well forget the Northern Beaches, Lower North Shore, Eastern Suburbs and The Hills...all are either too expensive or too far for you. Look at areas south, south west of the CBD like Hurstville, Padsto etc or maybe over the river to Jannali etc.

JAJ

Human Resource Adviser is on the list, as is Human Resource Manager (but that one is AIM assessed so is not necessarily going to be easy).
http://www.comlaw.gov.au/Details/F2011L01228

If the job can fit into one of these categories - or some other category on ENSOL - then the next question is whether a skill assessment can be obtained.

Alternatively, if the salary is high enough, (A$250k or more), then a skill assessment isn't needed.