This is a very interesting paper on married mothers labor supply, with a focus on the employment disincentives induced by child-related transfers.
Technically, it is a life-cycle, partial equilibrium model with two endogenous state variables: assets a and female human capital h. Households choose savings a', male and female labor supply l_m, l_f and next period human capital is given by h'=H(h,l_f). Fertility is exogenous and stochastic.
Unless I miss something, the model fits nicely into the setup of " Life-Cycle model 41: Female Labor Force Participation History (experienceasset)", codes available here:
The authors write in the appendix that they solve the model using value function iteration due to the many kinks and non-convexities induced by the detailed tax and transfer scheme. The toolkit then should perform quite well.