B.C.
Based on your criteria, I would go to cheapcaribbean.com.
My wife and I stayed at Secrets Silver Sands on the Mexican Riveria. We stayed there for 8 nights and had a blast. They have 6 excellent restaurants and is an all inclusive. My wife and I didn't do any shopping. We only wanted some souveniers. But the water and rooms and beach and pools were wonderful !
Cheap Carribbean specializes in 3, 4, and 6 day packages at almost any caribbean island so I'm sure you'll find something you'll like at a reasonable price.
Jamaica is also wonderful. I'd stay at a resort on the Montego Bay end of the island. There are lots of all inclusives there. There are lots of recreational possibilities there.
Good luck to you and yours. I hope you have a wonderful time!