G'day Wendyh
I see your options as being:
(1) Taxis (4 people) or Maxi Taxis (10 people) to suburban North Shore line (apprx $50-$60 each taxi one way) travelling to Hornsby and change trains there to Newcastle and do same on return leg. I don't know cost of train journey but estimate $25-$30 each.
(2) Ferry to Circular Quay (City) train from Circular Quay to Central Station (3 stops) and then train to Newcastle (1.75hrs to 2hrs for train leg), total time would be approximately 3.5hrs - 4hrs each way but nice way to travel as very scenic. Total cost approx $30-$35 each.
(3) Hire cars and drive to Newcastle about 1.5hrs to 1.75hrs from Manly.
(4) Have your hotel arrange a driver and a Mini-bus which may be expensive but worth exploring and I would have them book well in advance. This option may actually be competitive price wise when compared to public transport and much more convenient.
(5) Hire a van or mini-bus that can fit you all so you only require 1 driver. In NSW they will require a bus licence if seating over 10 people.
Warning: be conscious of the fact that Sydney to Newcastle trains do not run 24hrs so do not miss the last train if that is the way you choose to travel. Otherwise the first train departs around 5.00am, I think. The rail journey is very scenic particularly around Gosford area.
The road from Sydney to Newcastle is a big Freeway most of the way with a speed limit of 110kms/hr so is easy to travel on. Newcastle is a great town with friendly locals who are RL nuts and great pubs so I would spend time at one or two of those and fork out the cash for a driver. The extra cost when converted to pounds should be nothing for you guys anyway.
I hope this helps. Please post any more questions or queries if you require any clarification of above and I wor others will attempt to assist. Enjoy your stay.
Cheers