Many of the most important applications predicted to arise from Synthetic Biology will require engineered cellular memory with the capability to store data in a rewritable and reversible manner upon induction by transient stimuli. DNA recombination provides an ideal platform for cellular data storage and has allowed the development of a rewritable recombinase addressable data (RAD) module, capable of efficient data storage within a chromosome. Here, we develop the first detailed mechanistic model of DNA recombination, and validate it against a new set of in vitro data on recombination efficiencies across a range of different concentrations of integrase and gp3. Investigation of in vivo recombination dynamics using our model reveals the importance of fully accounting for all mechanistic features of DNA recombination in order to accurately predict the effect of different switching strategies on RAD module performance, and highlights its usefulness as a design tool for building future synthetic circuitry.