At that young of an age, you're effectively required to hire a private babysitter, at a truly luxury property.

FS Palm Beach will take kids into the Kids for All Seasons program as young as 3, but they must be potty trained. The FS-PB has one of the lowest minimum ages of any high-end hotel kids' programs in the US.

http://www.fourseasons.com/palmbeach...amily_getaway/

FS-Nevis will also take 3 year olds. Nevis doesn't have the potty-trained requirement listed on their website, though I suspect they require it.
http://www.fourseasons.com/nevis/ser...r_all_seasons/

FS-Hualalai is 5 years old as minimum, as is RC-Palm Beach.
http://www.fourseasons.com/hualalai/...r_all_seasons/
http://www.ritzcarlton.com/en/Proper...ns/Default.htm

Assuming it will cost about $75 for 4 hours of child care (perhaps do this once a day), when considered in light of the all-in cost of the trip, it's not really material.