Does Islamic law permit abstaining from procreation due to a lack of trust in the husband, owing to his indiscretions and grave misdeeds?

We have previously answered regarding the ruling on delaying childbirth for an excuse, such as the one you mentioned. A Muslim should not entertain ill thoughts about others unless there is clear evidence and a strong indication. The default assumption about Muslims is their innocence from any wrongdoing, and one should not deviate from this principle except with conclusive proof. One should not judge a person as bad merely because they have made mistakes a few times, for all humans are fallible, and the best of those who err are those who repent.