If you disable the default browser (safari) an alternate browser can be installed that has filtering and or monitoring capabilities. In such a case the wife would have to put on the password to disable Safari and not allow it to be reinstalled. You can then install covenant eyes or any other monitoring browser. You still have to verify there are no other 3rd party browsers, and that he is not resetting the device, and allowing Safari. The best thing is not allowing purchases in the app store, which also would have to be done by the wife.
Also, as i mentioned the history in safari itself can only be erased in it’s entirety. Therefore you can always check the history, if it is mysteriously showing nothing for the past few days then you know it was erased. If you can have an open conversation saying that you will check it periodically then he would avoid going to inappropriate sites assuming he cares.
It is a bit complicated but something everyone should be educated about if a family member has an iPad/iPhone.