The Inland Route from CHC to Te Anau is interesting, with plenty of places to stop along the way - depending on the kids interests. Canterbury Plains on SH1, not so much. Doing the Inland Route off a plane when you are also pressed for time is .... sub-optimal, IMO. I'd be dubious of anyone getting off a flight, wrangling children and a rental car and a data sim for the duration, and then driving that far on the afternoon of Day 1; Indeed, a number of rental car companies will refuse to rent to you if you mention that's the intention. I would also be dubious of staying in Queenstown. Wanaka (or even Cromwell) is far more pleasant all around. The drive from Te Anau to Milford is exceptionally pretty, especially if started before 8am, but it is also *very* weather dependent and, in places, quite technical.

For day 1, maybe as far as Geraldine on the Inland Route? Good motel options for over night, options for dinner and then the following morning tourist stuff with the kids (again, depending on their interests) if wanted, and/or then a pleasant & relaxed drive down to Te Anau. I can't think of a single reason to ever stop in Tekapo other than to empty your wallet there. Horrible place.

Te Anau - lots of nice motels in the town itself and everything within walking distance.