Lot's of things can slip through the cracks on the underwriting side - but get flushed out on the liability side later on......
Your daughter could not be added as a secondary if she does not reside with you and/or is not a student - so that is no surprise
In your scenario- I will say there are two things you might want to consider thinking about.
1. Your daughter has no insurable interest in the subject vehicle - probably not an issue since you're family
2. Your wife has no liability coverage under the policy.
Let's say you're daughter is 100% liable for an accident - there are serious injuries in the other vehicle - their counsel sues the driver, vehicle owner etc. - your wife is not party to the policy and you most likely will be funding your own defence costs