LutherElem,
Here is the solution:
Before updating the iPads, DO NOT update the apps from iTunes
1. Connect the iPads to the computer that has the AC
2. Open AC
3. Uncheck the profile that you pushed to the iPads, then click Apply
4. Now update the apps through iTunes, then add the updated apps and the new apps to AC
5. Check the new apps, then Apply
6. Check the previous profile, then Apply
Why?
Let's take a look at what the Apple Configuration (AC) will do when an iPad is connected. Below is the steps it runs through in order:
Retrieving iOS information-->Checking Activation...-->Checking Pairing...-->Installing Apps-->Retrieving Documents-->Installing Configuration
As you can see, it's installing apps first before installing configuration (the profile). If your profile was set to not to allow the iPad to install apps (meaning you removed the App Store from the iPad), the AC can't push updated/new apps to the iPad. That's why you can't update the apps from iTunes at the beginning and that's why on step 3 you need to remove your initial profile before pushing updated/new apps.
If the apps in the AC already got updated through iTunes or there were new apps in the AC, that will pop up the "Can't install apps" error. If the apps in the AC are still the same version as those in the iPad, it won't pop up that error. That's why we do not update the apps through iTunes at the first beginning to make sure the apps versions in the iPads are still the same as those in the AC.
To summarize again, the iPads need the Apple Store back before they can be loaded with updated/new apps by the AC. The profile installed on the iPads were blocking the AC to push updated/new apps. That's why we have to remove that profile and put it back in the end.
I feel I am making you confused. 🙂
I am not native English speaker, sorry that if I did not explain well enough.