Any option other recursive search possible to go from one 2d point to another point with fixed set of possible moves?
There is a simple method that is often faster: If you have $n$ moves to go from $A$ to $B$, determine the set of all points that you can reach from $A$ in $\lfloor \frac{n}{2} \rfloor$ moves, and the set of all points from which $B$ can be reached in  $\lceil \frac{n}{2} \rceil$ moves, and then find if there are points in the intersection of these sets.