Upvote:2
Your UK passports allow you to enter the UK visa-free (obviously), so use those there, and show your UK passports to the airline.
They also allow you to use the ESTA and VWP to enter the USA - so you'll use them there again (do remember to go online to apply for the ESTA beforehand).
The only times you'll need to use your ZA passports are:
- Leaving ZA (where you'll get an exit stamp)
- Returning to ZA (where you'll need to be re-admitted as residents, not visitors)
It's likely that neither the UK nor USA authorities will be at all concerned that you also have ZA passports (unless you've previously been refused a visa or denied entry while using the ZA passport) and there should be no reason to even offer or present the ZA passport when arriving in either the UK or USA.
When returning from the USA to the UK, you'll show the airline your UK passports, and you will probably want to show the airline your ZA passports when departing the UK to return to ZA, as that'll show them that you have the right to re-enter ZA and the airline doesn't need to be concerned about whether or not you'll be denied entry (requiring them to take you back).