Hi Amir,
Switching changes will take only effect for the first time only. So no removing the ambition pro theme and also reactivating the theme will not solve the issues because the settings for ambition pro is already setup in your data base. So the only way is you need to drag and drop all the widgets that you have added in your free version. We are sorry for the issues you got.
One thing you can do is download this plugins for widgets importer and exporter. Install this plugins in your dashboard and activate Ambition Free theme. Export the widgets using widget importer plugins. View below screenshot.
http://awesomescreenshot.com/0b25oeiq9a
Similarly, activate the theme ambition-pro and import the widgets content using the same plugins.
View below screenshot.
http://awesomescreenshot.com/03c5oej189
Hope this may help you
Thank you!