With the onset of the COVID-19 pandemic, parents had to reorganize their family routines under many external stressors (e.g., limited external childcare), which could have negatively affected their relationship satisfaction. This study aimed to examine the changes in relationship satisfaction of young parents from pre-pandemic times up to the second wave of the COVID-19 pandemic in Germany in December 2020 and whether these changes were different for mothers and fathers. Additionally, the role of perceived pandemic-related stress and changes in family routines was investigated. Data from 564 participants from DREAMCORONA, a sub-study of the prospective longitudinal cohort study “Dresden Study on Parenting, Work, and Mental Health” (DREAM), were analyzed. Relationship satisfaction was assessed at three measurement points (T0: pre-pandemic, i.e., August 2018–March 2020; T1: May–June 2020; T2: October–December 2020). To estimate changes in relationship satisfaction over time, Latent Growth Curve Models were calculated. Changes in family routines (i.e., changes in the division of housework and childcare from T0 to T1 as well as the availability of external childcare facilities at T1) and perceived pandemic-related stress at T1 were used as predictors. The models were adjusted for education and number of children per household. There was no significant change in relationship satisfaction over time, with no differences between mothers and fathers. The multi-group model revealed that changes in the division of housework and childcare predicted changes in relationship satisfaction in mothers, but not in fathers. For mothers, doing more housework than before the pandemic was negatively associated with changes in their relationship satisfaction over time. Additionally, reporting that their partner did more childcare than before the pandemic was positively associated with the relationship satisfaction of mothers. Our results indicate no general negative prospective association between the COVID-19 pandemic and parental relationship satisfaction over time. Nevertheless, our findings highlight the importance of the division of housework and childcare for mothers’ relationship satisfaction and how pandemic-related changes in family routines alter this association.