Quantifying the inheritance of protein regulation during asymmetric cell division remains a challenge due to the complexity of these systems and the lack of a formal mathematical definition. We introduce ODEinherit, a new statistical framework leveraging ordinary differential equations (ODEs) to measure how much a mother cell's regulatory network is passed on to its daughters, addressing this gap. ODEinherit first estimates cell-specific regulatory networks through ODE systems, incorporating novel adjustments for non-oscillatory trajectories. Then, inheritance is quantified by evaluating how well a mother's regulatory network explains its daughter's trajectories. We demonstrate that precise quantification of this inheritance relies on pruning and adjustment for the network density. We benchmark ODEinherit on simulated data and apply it to live-cell, time-lapse microscopy data, where we track the expression dynamics of six proteins across 85 dividing S. cerevisiae cells over eight hours. Our results reveal substantial heterogeneity in inheritance rates among mother-daughter pairs, paving the way for applications in cellular stress response and cell-fate prediction studies across generations.