We just returned from Beaches All Inclusive in Turks and Caicos - no kids, but would be perfect for kids. Downside - expensive. Upside - many dining options, incredible beach and multiple pools. Kids activities and kids club. Waterpark. They have a specific office where you can go and discuss special dining requirements like allergies that people report is responsive.

Try researching Marriott in Aruba. It's very kid friendly. We've been to Aruba over 10 times with our daughter who also has a peanut allergy. We have stayed mostly at the Hilton though. It's more low-key but has an awesome kids club "Shocoland". My daughter has loved going there for activities during the day. The people are so friendly. We have eaten at many restaurants and have never had a food problem. We mention the peanut allergy. I've never been to Turks & Caicos. I think Palm Beach in Aruba is very nice. Blue water and calm to swim in.

Turks & Caicos for sure, beautiful 12 mile beach, many dining options & restaurants are in tune with allergy requests IMO. Look at The Somerset on Grace Bay or The Sands on Grace Bay ( 2 price points) Somerset is higher end & Beautiful!!