I'm still puzzled by your apparent belief that adding your name or your son's name to your husband's passport would enable you "to travel abroad with him as needed." But here's what I can say without understanding that:
Most countries, if not all, will require each of you to have your own passport, whether any passport has anyone else's name in it or not. It's not terribly uncommon for family members to travel with passports from different countries.
The Netherlands stopped including children in their parents' passports on 26 June, 2012.
But they still do list spouses and partners in each other's passports:
Naam partner in reisdocument
U kunt de naam van uw partner laten bijschrijven in uw paspoort. Dit kan alleen als u getrouwd of geregistreerd partner bent. Dit is ook mogelijk als uw partner is overleden of als u bent gescheiden.
Partner's name in travel document
You can have your partner's name included in your passport, only if you are married or in a registered partnership. This is also possible if your partner is deceased or if you are divorced.
If you're listed in your husband's passport, you'll still need your own passport to travel outside of South Africa. Being listed in his passport might help you benefit from European Union freedom of movement as your husband's family member, but in most formal circumstances you would need your marriage certificate for that anyway.
If your son is also your husband's son, he is almost certainly a Dutch citizen from birth, and will be at least until he turns 28. He can easily extend this by getting a new Dutch passport before he turns 28; the actual rules are somewhat complicated, however, and beyond the scope of your question. The fact that he would be Dutch from birth, I believe, means that he would not lose his South African nationality under South African law if he applies for a passport, but you might want to ask that as a new question.
If your son is in fact a dual citizen of South Africa and the Netherlands, he will probably need a South African passport to leave and reenter South Africa, and he might want a Dutch passport to travel to Europe or to any other country where Dutch citizens can travel without a visa but South African citizens require one.
In short, you should concentrate on getting South African passports for yourself and for your son, and, if your son is a Dutch citizen, a Dutch passport for your son.