Both families thanked the emergency services and the local community for their help on Tuesday.
The Beaton family said in a statement issued by police: "Our focus remains firmly on finding Ewen and bringing him home. We would again like to thank everyone for their continued efforts to find him, particularly our dear friends in the local community.
"We would like to thank the police, coastguard, RNLI and all the other emergency services who did everything they could for little Ewen and Jamie."
The MacKay family thanked staff at Broadford Hospital on the Isle of Skye and at Yorkhill Hospital in Glasgow where Grace was treated.
"We can't believe what people have done for our family and we thank them all from the bottom of our hearts. We hope that the emergency teams can find Ewen, and the Beaton family is very much in our thoughts at this time."