Using Managed Play? Find it difficult to rush an emergency app update out?

Have a look at the app update policy in your mobile device management solution and look for something called a high priority app update. Using high priority you should be able to bypass normal constraints of auto updates to have the app updated as soon a new version is made available in Google Play.

Some information from Google regarding the topic:

You can specify the app(s) for which the updates would become high priority.

Read the caveats mentioned by Google. This updates the app even when the user is using the app so better not set this as the default for all app updates.