In this paper, we start with a variation of the star cover problem called the Two-Squirrel problem. Given a set P of 2n points in the plane, and two sites \(c_1\) and \(c_2\) , compute two n-stars \(S_1\) and \(S_2\) centered at \(c_1\) and \(c_2\) respectively such that the maximum weight of \(S_1\) and \(S_2\) is minimized. This problem is strongly NP-hard by a reduction from Equal-size Set-Partition with Rationals. Then we consider two variations of the Two-Squirrel problem, namely the Two-MST and Two-TSP problem, which are both NP-hard. The NP-hardness for the latter is obvious while the former needs a non-trivial reduction from Equal-size Set-Partition with Rationals. In terms of approximation algorithms, for Two-MST and Two-TSP we give factor 2.4268 and \(2+\varepsilon \) approximations respectively. Finally, we also show some interesting polynomial-time solvable cases for Two-MST.