Sorry that it's taken me so long to respond - haven't been on to BF for quite some time...
Obviously, the suggestions to head to one of the reserves near Kruger or actually Kruger itself are all great. You will definitely see most of your target mammals there.
If you are wanting to avoid the big traveling distances across the country and give your wife some wildlife in luxury, there is a reserve about 2,5 hours drive from Cape Town called Sanbona Wildlife Reserve which has the Big 5 too. Apart from Leopard (which is near on impossible to find in the Cape due to their preferred habitat of rugged mountainous regions), the others are all introduced. They are however free-roaming and, with the reserve being 54000ha in size, it is not always straight-forward finding them. It is one of those reserves where you get driven around, rather than being allowed to drive on your own, but if you give them a list of target mammals up front, they will do their utmost to find them for you. The reserve also has all the other typical African species like Hippos, Giraffes, Brown Hyena, Black-backed Jackal, Caracal, African Wild Cat, etc. It will also give you an opportunity (probably one of the best in the country) to see Riverine Rabbit, the rarest mammal on the continent and the 13th rarest in the world, as well as a reasonable chance (as these things go) of finding Aardvark. Check out www.sanbona.com
if you are interested.
As to the birding, most of the Cape stuff is very easy and you won't need a guide. Just pray for some good weather and the stuff at Rooi-els should be a doddle - they can be tough if the wind is howling...!
If you need any further info, you are welcome to email me or contact me via Facebook, as I check those a lot more regularly than BF.