Android app upgrade: Backup database, remove current app, install new

The new version of my app is far too different in design and in database. I want, therefore, to remove the old app completely before installing the new app. All this of-course while the app update automatically from Play.

The steps I was thinking about are as follows:

• Backup SQLite database
• Uninstall old app (provided version number is lower)
• Install new app
• Move data from old database to new app's database

I tried to do this on the fly in my DataAccess class, but the differences are to great. Can anyone give me some guidance on that? Is it possible?

Thanks