Substituting cayenne for red pepper flakes
Crushed red pepper flakes and cayenne come from the same types of peppers, and you can definitely substitute one for the other in terms of spiciness (most resources I've found say that you add about 1/2 teaspoon of cayenne for every 3/4 teaspoon of crushed red pepper flakes, or vice versa).

However, beyond the spiciness level they may not give the same flavor to the dish. In the particular recipe that you're citing, since it calls for sauteing the flakes some of the spiciness will be drawn out of the flakes and carried with the sauce, while some of it would stay with the flakes and provide those bursts of heat that your wife doesn't seem to like. As Willem says, you can use fresh chile peppers, add them like you would the flakes, and then take them out before serving. That is probably the closest you can get to the same flavor without having those "surprise spicy" moments. (1 red chile per 3/4 teaspoon flakes).

Adding ground cayenne pepper towards the end of the sauce would allow the sauce to have a pretty uniform spiciness, without any surprises, but may not give it the same flavor. Cayenne pepper is usually just the ground up cayenne pepper (a specific variety). Red pepper flakes may consist of a couple different types of dried red peppers, and they often include the dried up seeds in addition to the the dried peppers themselves. So, the cayenne will add the spice, but probably not the same complexity.

My suggestion: Make half the sauce with cayenne and half with red pepper flakes and see what you think!