Here's the thing. If the wife is 'dying to see the Amalfi Coast', then she's got it in her mind--maybe--that she wants to wake up in the morning, look out the window or the balcony or whatever, and see that iconic view, the houses on the side of the mountain next to the sea. That's what people pay for.
You will not experience that in Sorrento, although it is a better overall base. Problem is, the best way to get over to the A.C. from Sorrento is by SITA bus. And unless you really plan and catch an early bus from Sorrento to Positano, then to Amalfi-town, in late May/early June you will no doubt be frustrated by having to wait for two or three buses until your place in the queue is in front. And to me, time is money when you're in Italy.
So...even though I am usually a proponent of making one base rather than two, in this instance I would do two nights Sorrento, in which you can easily take the Circumvesuviana commuter train to see Pompei, Ercolano or Naples, or Capri by ferry during the day and come back to a nap and a great dinner in the evening. And then you & your wife can experience two nights in Positano, Amalfi or Ravello, or even Minori, Maiori or Cetara, and have those spectacular views described above.
Enjoy your planning!