Could The Birth Time Of A Child Affect The Parents Relationship?

Very much!
Lord krishna born under Rohini star. His uncle Kamsa harassed baby's parents vasudevar and Devaki with better harsher methods so they continued to remain in jail. It took 14 years for them to get released from prison.
14 years devaki was separated from her child.
(Because in previous birth she was kaikeyi made dasarath to exile Ram for 14 years into forest and thus Kousalya suffered separation from her child Ram . Kousalya born as yasodha in Gokulam - present Rsjasthan- enjoyed company of toddler Ram for over 14 years as compensation)
Thanks & Regards.
Happy MMXXIII.

 

The simple answer is no .
Many marital problems are because of misunderstanding between husband and wife . After childbirth existing problems may flare up because of partners unable to spend time with each other but that is ought to happen even without adding a baby since they were already existing . If there is a problem find a middle ground or find a counselor who can help you find a middle ground . Blaming it on timing of child birth will only increase hatred towards innocent baby . It is not baby who decided to come and separate the parents . life has ups and downs . During downturn focus on solving the problem or give it a time for it to reduce over period of time . Engaging mind where blaming things which are not in our control is only going to make the situation worst . Adults are responsible for their own problems.