How to model a logical indicator when two inequalities hold in Integer Programming?
Your general approach is a good one.  Use Boolean variable that captures whether an inequality holds to define $\delta_{i,j}^1$ and $\delta_{i,j}^2$.  Then, use Express boolean logic operations in zero-one integer linear programming (ILP) to define $\delta_{i,j}$ in terms of $\delta_{i,j}^1$ and $\delta_{i,j}^2$ (via a logical-AND operation).