I recently moved to the Caribbean. Personally I find there's lots to see and do on the 2 islands Ive visited so far so 3 islands in 2 weeks seems a lot to me.
For example we did Guadeloupe in 1 week and I want to go back as there's more things we didn't get around to doing. Eg we did canyoning, day on a boat, several different beaches, climbed the volcano, visited a beautiful natural site, swam to a local (small) island.
We didn't do several hikes which look interesting, or visit a couple of islands attached to guadeloupe. And obviously we only skimmed the surface of beaches.
In Martinique we've done many different beaches (different styles), several hikes (including to waterfalls and up the volcano), canyoning, boat trip to see dolphins, swum with turtles and beautiful fish (not on an excursion, they're just pretty easy to find), trip to a rum distillery, volcano museum, natural park. Trip on a quad. Sea museum.
We haven't yet visited a banana or sugar plantation. Or the slavery museum or the arboretum. I haven't done any nautical sports (sailing, canoeing, paddle boat, surfing, kite surfing...) though the DC have.
Anyway, I'd say 2 islands in 2 weeks if you don't want to stay in one place too long. There really is loads of things to do here.
Also bear in mind the HEAT! We tend to do activities in the morning but go home for the afternoon.
Also, next time in Guadeloupe we'll stay half the week on one side of the island and the other half on the other side to reduce time spent in the car.