I have an iphone 4 on 7.1.1 and an ipad mini retina which is a high end ios 7 device and I still think that 7 runs ok on iphone 4. Just restore the iphone, keep only 3 rows of icons per page and disable everything you don't use, or your father.
There's a fair bit of logic in this suggestion.
Instead of just arguing back and forth, just look at the facts.
Due to the vast number of satisfied users, there appears to be nothing wrong with iOS 7 on the iPhone 4.
It is often nothing to do with the OS but with an incompatible installed App.
Those who remember the days when ultra slow backups via iTunes were the scourge of the early iPhones will remember the solution was to delete all Apps and reinstall them one by one until the offending one was revealed.
That's why, in my opinion, rrares1996's suggestion is worth trying. Don't forget that not all Apps have been updated are therefore not necessarily compatible with iOS 7.