DR is probably the only island to find Kitesurfing plus most of your criteria. Maybe St. Lucia, too, though its much, much smaller and secluded. And gorgeous.
I would also look into Tulum, Mexico, maybe my favorite beach town. Not an island, but its in the Yucatan on the Caribbean, with some of the world's most beautiful beaches. Tulum is an area split into two: a rustic, secluded beach zone (many upscale places) and a more urban small town zone.
1) Yes there's kiteboarding.
http://oceanprokite.com/
2) Tulum is a getaway for many paid chicas from Mexico City; US, Canadians, Italians too
3) Still underdeveloped, though that's changing fast. If your girl from Peru is into Yoga/massage and stuff like that, she'll be very happy. Fantastic place to take girls.
4) You can drive up to Playa del Carmen (45 min) for a big pickup scene; Tulum is more chill, eco-upscale s---.
5) Its a much cheaper flight for you and your girl than most Caribbean islands.
6) 10 days is a while so you can also visit Chichen Itza, Coba, Uxmal and all the Mayan Pyramid sites.
7) You can also go to Merida for fantastic food and culture
8) The beach is f---ing unbelievable.
From a tactical perspective, this part of the Carribean allows you to venue change over and over and over and over to get your prey. You can literally kitesurf in the morning and hike through Mayan sites in the afternoon, get drunk or go to a UNESCO World Heritage Site Bio-Reserve 10 minutes down the road. What's her personality like? If she's adventurous she'll love it. If she's more princessey, maybe a resort, but that could get old after 10 days.
Good Luck.