Last year we stayed at Barony Beach with our 4 year old. He loved the resort and there were many activities for him all week, we got a schedule and he attended alot of the extras. We rented bikes for the week and used to bike up the road a way and go to one of the mini golf places, that was fun. We enjoyed fireworks one night with lots of kids activities at Shelter Cove. You shouldn't have any problems keeping them occupied there!
I agree with the other posting that there is a lot to do with children on Hilton Head but if you come again Marriott's Grand Ocean or even Monarch they are in a better location for young kids. It is easier to bicycle with little or no traffic at the Sea Pines end of the island. There are bike trails that lead you through Sea Pines from Grand Ocean. Also Grand Ocean is less spread out if you are walking with very young kids. You can tell I love Grand Ocean. I own two weeks there and have grown kids. Enjoy Hilton Head. .