There is a not a single answer to this questions. Its imperative to understand how a team should perform so that you can spot dysfunction and respond appropriately. You need to understand the dysfunction to address the problem.
One resource that comes to mind is the book "the 5 dysfunctions of a team".
While what you mention initially sounds like "avoidance of accountability" and "Lack of committment" this may come from a deadline that is ridiculous or other requirements that are overbearing but because there's an "absence of trust" the team can't talk about the issues and things end up derailing.
I suggest you refocus yourself as a leader of people (regardless of your title) which is much more than a manager (of anything, people, projects, deliverables, clients, etc). It is how well you are able to lead that affects the performance of the team and acceptance of the client.
Driving the team through control will fail and backfire as you'll invite the bottom four items in the pyramid. Servant Leadership will serve you better. (think agile, read about scrum master principles etc). Anything from John Maxwell on leadership is a good read.
Another resource I'd suggest is "Extreme Ownership - How Navy Seals Lead and Win". It highlights that given two teams - one high performing and one low performing - swapping leaders shows that performance follows the leader (chapter 2 - No Bad Teams, Only Bad Leaders).