This is a sort of negative-leaning answer to the question about existence of software for your purpose.    There is quite a bit of history to the problem in prime characteristic, going back to isolated examples found in the late 1970s by Mumford and a student of his which showed that the classical ideas could break down.    The rank 2 example $G_2$ lends itself to picture drawing and has been looked at in considerable detail.   See the recent updated preprint by Andersen and Kaneda <a href="http://front.math.ucdavis.edu/1107.3055">here</a>.  

Andersen's clever sheaf cohomology techniques (exploiting the Frobenius map) combined with my more speculative predictions tend to imply that the results depend heavily on Kazhdan-Lusztig theory for the affine Weyl group (of Langlands dual type).   Moreover, the non-vanishing of cohomology seems to involve the actual module structure, so dimensions appear only as a byproduct of the study of generic module filtrations crossing Weyl chamber walls.   The algebraic group of type $G_2$ already indicates how systematic but complicated the results will be in general, so any computational approach must take this case into account.  (The results for $A_2$ and $B_2$ worked out by Andersen following his 1977 MIT thesis work are also subtle, but con't compete with the complexity of $G_2$ whose alcove geometry is richer.)