I'm sorry if this is presumptuous, but the questions about jet lag were completely buried in the other thread. I thought it was unfair to the OP, and others who had chimed in with similar travel arrangements.
I think it affects people differently, but it's quite likely that you'll get hit on at least one of the journeys. Best to plan for some down-time upon arrival, so you can catch up without stressing about it. Also: PLEASE don't drive on the first day. Get an actual night's sleep first. Accidents can involve other innocent people on the roads!
We were lucky, we only had a mild jet-lag upon arrival in Auckland. We'd had a long lay-over as well, and arrived in Auckland just after noon. We felt fine, fit even. We went out, walked about and explored a bit. We got hit after our early dinner and had to force ourselves to stay awake until it was dark outside (in March that wasn't very late, thankfully). We slept very well that first night. The next day we were noticeably less alert/fit, but it was mild. That second night had us waking up at a stupidly early hour in the morning, but we'd gone to bed fairly early so we felt rested. Still a few lingering cobwebs/sleepiness (mainly in the afternoon), so we were VERY happy we were only driving a short while. That last bit of jet-lag and the unfamiliar driving/vehicle was enough to tire us out quickly. Note that we didn't get behind the wheel until our third day in the country. I was very happy with that planning. From there on, we slept well and felt normal.
I have no idea how much it actually helped, since I don't have an alternative to compare it to, but we set our watches to destination time the moment we boarded the plane. Sleeping was not the easiest on a day-time flight, but with noise-cancelling headphones, sleeping masks and good pillows it sort of worked. The headphones were worth every penny, we will not travel without them anymore.
Our layover was during the local daytime, so we went out. Keeping busy means you become tired, which was useful since it meant sleeping on the next plane was easier. Again, watches set to NZ time once on board. We got up to stretch a few times, drank lots of water and avoided simple carbs (both on the plane and the day before traveling). It's the usual advice, but it did help....