Be warned, the Rod Stewart Musical finishes on Saturday the 6th, and the evening tickets are showing as limited. If you want to book your tickets in advance, they Mayflower has an agent on the web https://www.ticketsouth.co.uk/may/ShowDatesCombo.aspx
We're not familiar with the Hunter's Lodge, from looking on the web, I presume it's the one in Languard Road, if so, it has an AA 4 star rating, and is as good a place as any to be in Southampton, as it's within easy walking distance for everything. I take it that you've seen their website http://www.hunterslodgehotel.net/index.htm
For the Isle of Wight, it's a short crossing from Southampton, and passes close to the QEII terminal - unfortunately you leave on the day that the QEII arrives, and the day before the QM2 arrives, so won't be sailing past them.
To go to Winchester, you can simply hop on a train (10 minutes from your hotel) which will get you there in about 15 minutes depending on number of en-route stops. The way to the centre of Winchester isn't at all obvious from the station, so it's best to ask at the desk. You may also want to stop in at the military museums & old gates on the way into the city. Again, just ask if you want more specifics.
As for shopping, Cindy will be pleased to know that Southampton has a new shopping centre - West Quay - so be warned ;o)
best wishes to the two of you,
Alan & Katrina