Using apps on one device with different Apple ID's I was wondering, if I login to the app store with a different Apple ID on a device, will I be able to still use the apps on the device not downloaded or purchased from the current Apple ID?

Example: My wife has an iPhone with many different apps she's downloaded. If I took her phone, logged out of her app store Apple ID, then logged in with my Apple ID, and downloaded other apps, would I be able to use the apps she already downloaded on the phone without having to log her back into the App Store?
iCloud Family Sharing is perfect for this situation.

https://www.apple.com/icloud/family-sharing/

It allows you to share each others apps, pictures and purchased media without any issues.  It works pretty well in our experience.