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That sounds great! I'm sure you'll love Tasmania. If you're planning to base yourself somewhere on the Island and do day trips from there, I would recommend Hobart and Launceston as two of the better travel hubs.
https://news.experienceoz.com.au/hobart-travel-guide/ - This might help for Hobart
https://news.experienceoz.com.au/launceston-travel-guide/ - This should come in handy for Launceston.
You'll be able to see most of Tasmania within 1-2 weeks, possibly 10-14 days would be ideal if you're looking to take it slow.
As far as things to do other than wineries, hiking trips or water sports, I would suggest checking out Port Arthur (https://news.experienceoz.com.au/top-5-things-to-do-port-arthur/), Cradle Coast (https://news.experienceoz.com.au/top-5-things-cradle-coast/), and the Bonorong Wildlife Park is also really good (https://www.experienceoz.com.au/en/hobart/bonorong-wildlife-sanctuary).
There are also some great museums, such as the Museum of Old and New Art (MONA) or you could check out some of the foodie experiences at Bruny Island, which have tours leaving from Hobart;
These are two tours at Bruny Island which include a lot of food and scenery (https://www.experienceoz.com.au/en/hobart/bruny-island-full-day-tour-including-six-courses-/bruny-island-full-day-tour-including-six-courses)
We hope you, your daughter and your mum have a wonderful time in Tasmania and if you book into some experiences we’d love to see some photos. Also, if you have any questions about some of our products don’t hesitate to online chat or call our reservations department.