For my tuppence worth, you have three separate photographic requirements; game drive; landscape and cityscape/travel. Factors that will affect the final choices , particularly on the safaris will be
1. The baggage weight limit on the charter aircraft. Often it is 15kg per pax on the smaller aircraft, so best to double check your carriers limits. Judicious sharing of kit and carrying the odd lens or body in your jacket can stretch these limits. You will need to factor in the rest of your luggage also.
2. Type of vehicle. Mandikwe vehicles appear to be the standard South African style with a roof covering. That is either two rows of two or three rows of three from the images on their safari site. sitting in the row behind the driver gives good viewing, more foot/floor space and also reduced bouncing than sitting above or behind the rear axle. 10 pax will need at least two vehicles. Work from the lesser crowded vehicle to maximise space for you. If space is tight then leave the camera bag at camp and carry you cleaning kit and blower and perhaps one lens with you in a jacket of vest. I try to avoid changing lenses unless absolutely necessary to avoid dust ingress into the body.
3. Your photography on safari will be from the vehicle. Two bodies which are strapped to you is a very workable option. Loose cameras are likely to get damaged as the vehicle bounces around. (I learnt the ahead way). Lens choice will depend on whether the safari vehicles can of off track or not - contact the camp to see. Basic set up longer lens on a camera with a high shutter speed and performance for distance/smaller/ moving subjects and a medium lens on the second body for closer, slower / static subjects. the 400 on the 0M-1 doesn't offer. crop mode option which means you are limited to a max of 400 which is could be a tad short if the vehicles stay on tracks. and the savannah is open (Z9 with 70-200 + 1.4 tc in crop mode gives you 420mm f4)
4. Whilst animals are often the main attraction, landscape and scenery, particularly the big skies are not to be missed. To that end anything from 24mm upwards will suffice.
5. Shooting with a long lenses to close distance will very likely result in soft images from heat haze and dust. Filling the frame and where safe, getting close will negate this and result in sharper images
6. It doesn't appear to be a photo safari and as you are with your family a zoom gives you far more flexibility than a prime as moving to get you into range for the 800mm may not be to everyones liking whereas a zoom provides a variable range than caters for the vehicles positioning and also any animal movement.
OM-1 with 100-400 is one option (although the Z9 with 70-200 and tc gives 98-280 and 147-420 in crop mode) and if off roadable and there are larger animals the z8 and 24-70 (which also gives 36-105 in dx mode) covers many bases. from 24-420. If it's too close for the 24-70 then its time for the smartphone!
Victoria Fall
Photographing around Vc Fall is dependent on time of year, currently the water flows will be lower meaning you can get a wider range of images along the length of the Falls. Here is the link for what I believe is the best info site for anyone visiting the Falls.
Taking photographs at Victoria Falls certainly poses many challenges, Detailed here are some useful tips that will help you.
www.victoriafalls-guide.net
I throughly recommend a sunrise or sunset cruise on the Zambezi river not only are there plenty of wildlife, birds in particular, but the scenery and landscape are spectacular.
The Z8 with 24-70 and the 70-200 would be a useful combo. Having the 14-30 adds little weight or bulk.
Cape Town
Great Opportunity for street/travel photography around Cape Town particularly around the muslim quarter of the Bo Kap area, as well as landscapes from Signal hill. Interesting seascape can be got from from Blouberg beach across the bay to Table mountain. The V& Waterfront offers some great shopping and photo opportunities for half a dy. I am an advocate of carrying less in cities and carry one body a wide angle and a short - medium telephoto which covers most bases as changing lenses is easier (providing it's dry). if you are using a vehicle that is nearby or has some with it then you could possibly consider leaving a second body and lenses in the boot rather than carrying a second body around and simply select what you need dependent on the venue/location. I tend to plan for a specific type of venue and take the minimum I can. If you want do some macro then the Kirstenbosch gardens may be up your street. Be mindful of who is around you, big city security awareness etc. Low profile discretion works well in the city centre.
For travel and street the OM-1 with 12-40 is relatively compact. Agree landscape benefits from full frame.
I would plump for the Z8 and the 14-30 and the 24-70 which will be a workhorse lens. The lenses focal length will determine the body. 100-400 is a very useful wildlife and landscape focal range which dictates the OM-1 being used whilst you have some great focal ranges with Nikon. regardless of what you decode to take, the best camera is the one you have with you when you need it. Have a great trip, you and your family will love the experiences