I'm in SA but not Joburg, PIL in Joburg and love it. They don't have kids though.
In terms of you working, you really need to look into visas. DP is South African, so technically I am allowed to work - in reality, it is near impossible to work. It took me 7 months to get a spouse visa, and I would need to get a company to sponsor me, prove a local cannot do the job and then add an endorsement to my visa. Sounds easy in practice, however I was told that this takes 9 months - a job won't be open for that long.
A friend who is here as a spouse of a non-South African is not allowed to work as part of her visa conditions.
Safety-wise, we and PILs have never had issues. Like most places, there are areas you avoid and you take extra precautions. His company should be able to help you set up with an external security company.
The MD of DP's company is British, came over here a few years ago with his wife and 4 kids who were similar ages to yours and they have just thrived. They are outdoors constantly, very in touch with nature, have been skiing etc. They do live fairly far out of Joburg in a gated community so that they have a big garden, pool etc. The husband has a fairly busy commute with traffic etc but this is normal for JHB.
They are many groups in Joburg for trailing spouses/expat wives. The wife of the MD is heavily involved in charity work so that is definitely a possibility.
Sorry I can't help much with package, school fees etc. But it is worth looking into, it is such a beautiful country with the friendliest people. I am leaving soon and devastated that I have to!