Is there any publicly available software to simulate this or some other method to see if one substance can be dissolved by the other (and preferably to see how fast)?
Sure, this is done all the time in predicting solvation free energies using molecular dynamics.
We also compare the performance of absolute solvation free energies obtained using the OPLS_2005 force field with two other commonly used small molecule force fields—general AMBER force field (GAFF) with AM1-BCC charges and CHARMm-MSI with CHelpG charges.
The solvation free energy is computed as the sum of three contributions originated at the cavitation of the solute by the solvent, the solute-solvent repulsion and dispersion interactions, and the electrostatic solvation of the solute.
The basic idea is that you use MD (and either a good force field or quantum chemical method) to simulate the molecule in solvent and consider the relevant thermodynamic cycle.
For the most part, the focus has been on the thermodynamics, not the kinetics. In principal, you could start an MD simulation with a solid packing of your molecule of interest and your solvent (e.g., water) next to it. In that case, you'll probably want to do some sort of weighted ensemble MD calculation to get accurate kinetics of the solvation process.