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Antihydrogen atoms, H―, are now routinely created and can be stored for long enough to allow comparison with ordinary matter. A major goal of these efforts is to test potential physics beyond the Standard Model. This will require further developments in the experiments including the accumulation of more antihydrogen atoms and their storage over longer times. The latter is limited by the unavoidable presence of normal hydrogen molecules. Interactions of H― with H2 lead to the destruction of the hard-won antimatter. Little is known about these interactions but quantitative information will be crucial in guiding experimental developments. Physically realistic modelling of rearrangement scattering of “heavy” antimatter particles (antiprotons, p―, and antihydrogen atoms) by normal matter molecules, such as H2 + H―→ Pn + Ps + H (where Pn represents protonium and Ps positronium), requires the development of new theoretical and computational methodologies. R-matrix theory offers a strong prospect for tackling such problems having proved itself in atomic, molecular and optical physics. It divides the problem into a computationally demanding but energy-independent inner region and simpler energy-dependent outer regions. We propose to adapt the new RmatReact ultracold chemistry approach for the more complex molecular matter-antimatter problems. Here, developments required for the inner region, the boundary and outer regions are outlined. We also report some preliminary bound-state calculations on the {p,p,p―} system and a study of the required mixed coordinate systems for the general effective 3-body case and their transformations at the R-matrix boundary surfaces.