Serabee
Autistic Time-Traveler
This is an extremely old post (from around when the DLC was released, looks like), but I'll still clarify:I know that for designing, you should access Happy Home Paradise, and there are two options to do that.
The OP asked how to remodel homes on their own island, not just build vacation homes. This is a feature that is unlocked after you complete the "main story" in the DLC, which IIRC, takes about 30 homes designed, as well as all the public buildings done at least once (you don't need to add more rooms to the hospital or do the gallery on the cafe).