South Island Winter recommendations for a family

Hi All, I'm a complete newbie - not just to the site, but to the country - so local advice would be really welcome. Apologies in advance for the long post. We're an Irish family of 5 - our kids are aged 14, 12 and 10. We're in Auckland for a few months for work, and are taking hols on the South Island for the first two weeks of August. We're hikers, it's what we always do for our three week annual family holidays. We go the Italian Alps or Dolomites or Pyrenees every year, but always in summer. We (the parents) have decent Alpine experience and even did an Alpine mountaineering course in Switzerland many years ago. My husband climbs to AD standard, I'm more of a F/PD- type (I don't know if that grading means anything here). My husband has done a bit of Scottish winter climbing, but I haven't. The kids are fit and strong, and our eldest has done a little bit of glacier work on a rope with crampons, but nothing serious. Anyway, we're wondering what's safe for us to do here. We left our ropes, ice axes and crampons back in Dublin. We're not really into strolling along a valley floor (although of course we'll do that if there's no safe alternative). So a couple of questions: (1) Any suggestions for good winter day hikes that would suit us? (2) We'd love to do a hike to a hut that we could stay overnight in as the kids love that - we were thinking of the Kepler track to the Luxmore hut and back to avoid avalanche prone sections. Do we need axes and crampons for that section? General advice also welcome - thanks!! Aedin.