I agree about sticking to just one island, otherwise you will spend all your time rushing around and on the road.

Rotorua does have the highest concentration of mudpools, but there are some other areas that are less touristy like the Craters of the Moon walk just north of Taupo. There are numerous places with thermal vents/hot pools. I can't think of anywhere else that has a Maori culture centre.

As for North Island wineries, there are a few in Martinborough (on the other side of the Rimutaka ranges from Wellington). I haven't been there but I hear good things about it.

You can also do the Tongariro Crossing which is possibly the best day walk in NZ. It is 6ish hours though so you have to be reasonably fit and it would only work if the kiddies are happy to go in backpacks (with breaks). It is about an hour south of Taupo and crosses the bottom section of Mt Ngauruhoe which was enhanced to be Mt Doom in LOTR. This is the area that I live in.

Good luck deciding.