For a family I would recommend the best line for families - RCI. They have Splendour of the Seas sailing out of Venice for a week. Nice little friendly ship. For a longer cruise I would recommend my personal favourite in RCIs fleet - Brilliance - she sails from Barcelona for 12n.
Before you do anything at all please check that you can get insurance for all members of your party. All Cruise lines REQUIRE that you have medical insurance up to at least £2millon to ensure medical repatriation should it be necessary. If someone takes ill on a cruise that person will be offloaded at the next port. That will also impinge on all the other members of the parties Insurance as well. I have had the most terrible difficulty getting insurance for my 89 year old father in law. (£750 for 12 days) and we are UK residents and part of the EU which has reciprocal health arrangements. You, I note, are from Australia so I dont know how that will affect your party. I have been on 2 cruises where a medical evacuation by helicopter has been made and the other members of the party (including wife/husband)have had to remain on board until the next port. They then have to make their OWN way to wherever the helicopter took their relative to hospital.
If the elderly members of your party are UK based then I would suggest going on a cruise from a UK port such as Southampton returning to Southampton as flying with both young and old can be exhausting for all concerned! At least you know there will be no long waits, delays or potential DVD to contend with. I have read on this site that RCI often DO NOT provide DIRECT flights. If you go on a DIRECT flight from UK it is 3 hours at the airport plus 2hrs to western med/4 hrs to eastern med plus 1 hour approx to get to ship. I.e 6 to 8 hours travelling there and back. P & O has lots of cruises out of Southampton and are very family friendly. They have fully qualified nannies to look after young children (not just 'youth crew')and even have a night nursery till 1 or 2am so nightclubs and late dining are possible. Waiter served restaurants also make it easier for the elderley. Children also have their own dining time.
Finally check the temperature at the time of year you want to go. In high summer, not only are med destinations crowded, it is very hot making life difficult for the very old/young. The Greek Isles are wonderfull in spring(april/may) or autumn (october)and usually have cooling breezes. It is also easier to get to the sites of interest as everything is closer to the ports. Factor in taxis for trips as they are cheaper for families than ship excursions and are also easier to get in and out of if you are elderley (steps up to coaches can be impossible to negotiate for many). Have you considered the Canary Isles/Madeira? P&O have 7 day cruises to spain/portugal/france, Fjords in Norway, spain/fr/guernsey or sp/fr/ireland, 9/10 days to canary islands and Baltic. All med cruises are mainly 14 days. Hope this lengthy answer helps !! Whatever you decide have a wonderful time.