Osmo only recognizes the Apple ID that was initially used to purchase the app. Osmo app purchases aren't currently compatible with Apple's Family Sharing feature.
We are working with Apple in order to make our apps compatible with Apple's Family Sharing feature in the future, but we don't currently have a timeline for when this will be made available.
In the meantime, you can download the apps onto other iPads and restore the purchases by signing in with the Apple ID that was initially used to make the purchase. Once the apps are downloaded and you have signed in to your myOsmo account to restore the purchases, you should be able to sign out of that Apple ID and sign back in with a different one.
We suggest contacting the Apple Enterprise Tech Support group at 866-752-7753 as they should be able to help resolve the issue.