This is an unenviable position. I'm not sure there are any good/easy answers.
Who is accountable in this scenario?
Who approves the changes? Changes (last minute or not) have a financial impact on the company.
What is the change control process? It isn't clear whether the 3 PM's who communicate with the clients have the authority to unilaterally ...
There are two parts to your question:
Do the clients really need to make changes at very short notice
If this is a real need, what do we have to do to respond to changes very quickly
I would start by speaking with the clients and explaining the impact of last minute changes, which might include:
Efficiency lost due to context switching (i.e. shifting to ...
Without understanding fully, I don't think we can suggest the best approach. With that in mind, here is my approach based on the information given.
1) Remove the concept of 1 week development, 1 week testing. It should be test as soon as developed, fix bugs as soon as it is tested. This will ensure that your deliveries have as little amount of bugs as ...
If you can make this work for your teams then that is fine.
I would caution that a global definition of done has several drawbacks, including:
Getting consensus over several teams is challenging. If not all the teams agree with the final solution then they may ignore it or work around it.
Some aspects of the definition of done may be specific to each team.