The net swelling dynamics in molecular responsive hydrogels can be viewed as an integrated effect of discernible processes involving transport of actuating species, reaction with network components like destabilization of physical crosslinks or cleavage of network strands and concomitant network relaxation. Here, we describe a finite element modeling approach coupling these interdependent, underlying processes in hydrogels including oligonucleotide duplexes as physical crosslinks that can be destabilized by a particular molecule. These molecular responsive hydrogels based on acrylamide including either DNA or oligomorpholinos (MO), a DNA analogue, as functional elements can be made with various content of dsDNA or dsMO supported cross-links. The dsDNA or dsMO integrated in the hydrogel can be fabricated with ssDNA designed to competitively displace the connectivity of the dsDNA supported crosslinks, and similar for the MO hydrogels. The overall processes can be framed in a diffusion-reaction scheme. This process is dependent on the concentration of the diffusing species, their diffusion coefficients and their location. Thus, the reaction taking place in particular molecular responsive hydrogels is coupled with the deformations due to swelling and mechanical constraints undergone by the gel. Numerical examples show the importance of coupling reaction-diffusion with mechanical deformations for such gels. Finally, our model is compared to swelling experiments of hemi-spheroidal molecular responsive hydrogels bound to an optical fiber. Parameters of the reaction-diffusion model were obtained by fitting the model to reported experimental data where molecular stimuli designed with different molecular parameters for the competitive displacement reaction were employed in the swelling experiments.