Owner requested an overnight stay at my place But wants me to come to his place

Just let the owner know that it is either one or the other. Tell him/her "if you want me to walk your dog twice a day it is X amount. However if you would like to have Fido boarded at my house it is X amount." Then let him respond with their choice but don't budge. They are trying to pay you less by getting the boarding fee but you are doing the visiting twice a day which would be more.