Hi Bec,
I like your plan because it is visiting all my favourite places. I do have quite a few suggestions, but no major alterations.
My main suggestion is to not underestimate the length of your drives. One quite a few of your days you have a lot of activities planned, plus a drive. My suggestion is to view the drives as the activities. NZ roads are slow and windy with MANY places to stop to take photographs or go for short bush walks. The drive from Wanaka to the Glacier Region, for example, could potentially take you all day (and an awesome day at that).
My suggestions in Red
Sep 30 - Arrive Christchurch 3:20pm
Pick up campervan and a few supplies, if weather/forecast for following day is clear drive out to Banks Peninsular, spend night somewhere like Little River. If it’s not clear spend night at a campground around Christchurch somwere.
I would probably stay overnight in ChCh and skip the Peninsula on this trip. By the time you arrive, pick up the camper, get to a supermarket and then to a campground, it will be gettting to dinner time. If you stay in ChCh you can begin early the next day on all your planned activities.I really like the Top 10 holiday park, good for a 2 year old, it's near a mall with a good supermarket and is an easy drive from the Airport, I think you'd be pushing it to drive out to Banks Peninsular and appreciate it, to do anything in CHCH the next day you'd need to leave early.
Oct 1 – Spend some time around Banks Peninsular (if we’re there). Drive back into Christchurch. Activities again will depend on weather - Orana wildlife park
This park involves quite a bit of walking, you can hire a buggy or carry your little one, I'd say at least 1/2 a day though , Christchurch Gondola, Spencer Park, Tothill’s Mazes. Spend night around Christchurch.
I would hit the road late afternoon and spend the night just outside ChCh. Perhaps Rakaia or Ashburton. That way you can get going early the next morning for Mt Cook without contending with ChCh traffic. Having this head start will mean that the roads are quieter and more peaceful. I agree, I'd probably do Orana park last as it's on the outskirts and not backtrack into town.
Oct 2 – Drive to Glentanner Holiday Park Mount Cook. Stopping on the way to spend some time at Lake Tekapo. May do stargazing tour.
Definitely stop in Tekapo for a few hours. The church and lake are lovely, as are the hot pools. If you have a self-contained camper (highly recommended) I think you should stay in White Horse Hill DOC campground instead. Glentanner is quite a nice area, but nothing beats waking up at the foot of the mountain watching the sun rise behind it. Also if you head all the way in Mt Cook Village, you will be able to explore the area that afternoon. Know that there are minimal facilities in the area and restaurants are quite expensive. The attraction is the stunning views.
Driving into Mt Cook, take the small road past the Salmon Farm. It has the most stunning views of the mountains and Lake Pukaki. I will try and find a link to this road for you tonight. It's an easy road to miss.
Oct 3 – Take in the sites around Mount Cook/Aoraki - Hooker Valley Track and/or Kea Point Walk. Drive to Queenstown, spend night at campground.
Head off in the morning. Stop at Arrowtown on the way - I love it there. Do some Queenstown activities in the afternoon.We have easily spent a day at Arrowtown, it's one of my favourite places
Oct 4 – Activities in Queenstown - Odyssey Sensory Maze and Sunshine Bay Walk. Drive to Te Anau and spend night.
Drive through to Te Anau around midday. If you can do the glowworms (not sure about the age limit) do them this afternoon/evening
Oct 5 – Milford Sound coach tour (hasn’t been booked yet, still trying to decide which one to do, hopefully it’s not booked out by the time we decide). Return to Te Anau for night.
Oct 6 – See Fiordland National Park, tour a glowworm cave – can anyone recommend if one of these tours would be suitable with a 2 year old in a carrier on either mine or my husband’s back? Drive to Wanaka for the night.
Get going to Wanaka in the morning. Take your time driving over the Crown Range. It is steep and windy, but has a beautiful view from the top. Do Puzzling world in the afternoon. The playground and lake front are also lovely.
Oct 7 – Spend some time at Puzzling World before driving on to Franz Josef Glazier – what are some walks we can go on here? Hot pools. Spend the night.
Make a day of this drive. It's a long one but has great places to stop for short walks. I will email you a whole list of short walks tonight if you are interested.
I would recommend staying the night in Fox Glacier instead. My favourite walk in the whole country (Lake Matheson) is there, but it is best done late afternoon or early morning before the winds pick up. Also the weather changes from hour to hour in that stretch of the country. You need to allow a bit of time to wait out the weather should it be bad when you arrive.
I should mention that the Lake Matheson walk is about 45mins. What is the longest you can carry your little one on your back?I agree, we got flooded in to Franz Josef when we were there.
Oct 8 – If we didn’t get to do anything the day before that we still want to do, it will be done today. Drive on to Greymouth. Spend the night.
Drive to Franz josef, visit the Hot pools and do a short walk to see the Glacier. Carry onwards to Greymouth. I should mention that while Fox and Franz are close together there is a fairly steep mountain road between them. It is not ideal to backtrack if you decide to spend the night in Franz instead. [
I would consider driving further north and going to Punakaiki and see the pancake rocks & the blowholes, there is a small campground here and then you could return via Arthurs pass
Oct 9 – Drive to Christchurch. Doing anything that we missed from start of trip.
Allow at least half a day for this drive. Arthurs Pass is stunning and you will want to stop regularly for photos.
Oct 10 – Drop off campervan. Fly to Rotorua. Hire a car. This part of the trip hasn’t been booked yet, but essentially what follows is where we’re planning on being. We’ll be staying in hotels.
Oct 11 – Rotorua
If you check out my PTR it has my latest trip report from Rotorua, I would probably do things a bit differently feel free to ignore me 
Oct 10/11 Rotorua -lots of amazing things to do, the farm tour at the agrodome is good with young ones, my two year old loved the luge, Rainbow springs is good to see the Kiwi & Tuatara.
Oct 12 drive from Rotorua, stop at Wai-o-tapu -amazing natural spot, I think the best of the thermal areas. From there to Waikite hot springs, lovely natural hot springs great value and far nicer than any of the ones in town. Drive to Wairakei, there's a nice little maze/puzzle world on the way stay the night at Wairakei resort? Wairakei also has hot pools and is child friendly
Oct 13: The next morning do Craters of the moon and any other Taupo activities that interest you. Drive round the bottom of lake Taupo and head north past the mountains on State highway 4. Stop at Waitomo for the night, see the glowworm caves - beautiful.
Oct 14: The next morning head to Auckland
Oct 12 – Drive from Rotorua to Coromandel
The Coromandel is lovely, but is not always it's best at this time of the year. Definitely visit if you are keen, but an alternative option could be Taupo. This will give you a bit more time in Rotorua which I think you will need.
Oct 13 – Coromandel
Oct 14 – Drive from Coromandel to Auckland
Oct 15 – Auckland
Oct 16 – Fly out of Auckland at 8am.
Other than that, make sure you keep your petrol tank topped up. There are long stretches without stations and gas is very expensive on the West Coast. As are food supplies. Your best places for getting groceries are Christchurch, Queenstown and Wanaka.