I think it depends on the laws in your state. If one is under 18, states have been passing laws that if a gun owner doesn't lock their firearm and a minor ends up harmed because of it or is able to access a firearm because of it being left unlocked and use it in CTB, the gun owner can be charged.
If the person who accesses/uses a gun that is not locked in a safe or other method is an adult, I do not know what the possible law around that is.
But, some states are now passing laws that it is illegal to not store your gun in a locked way while you are not using it. And adding new laws to gun & firearm ownership in recent years.
I don't know how storing ammo in a separate location could affect possible charges in the case that it was illegal in your state to leave the gun unlocked, but it would probably be in your dad's favor.
I went to a gun safety course in the past where they taught about rules in my state, but it is very complicated and basically dependent on each individual case. And even if for example, something was illegal, sometimes police will be more lenient with certain people and more strict with other people. (This is my own observation from reading articles about cases and news stories.) And if there's a court case, the outcome would also depend on the opinions of the jurors and what their final decision was.
What I'm trying to say is, someone could be in a situation where they have done something illegal (even accidentally), but there are so many factors that go into:
1) whether they would actually be charged with something,
2) if it would be a severe charge or lowered to something lesser based on their lawyer's skills and the judge's decision
3) and what the opinions of the other people contributing to the final decision are (investigating police officers, jurors, judge, public opinion which people involved in a court case are usually not allowed to look at or read news articles about, but I don't know how strictly the court makes sure that actually happens.)
So, hypothetically let's say it was illegal for your dad to leave the gun in an accessible place. It's possible that after the final outcome of a court case, the people involved would decide that he should not be charged based on the circumstances. And in the end, he wouldn't end up in legal trouble after they came to that decision. Or it's possible that they would decide he should be charged with something.
Since we can't predict the future or know the opinions of the people who would be involved if a court case did happen, even if there was a law broken by your dad, we can't have a definite answer for whether he would get in legal trouble.
Also, I am not trying to be rude. Just emphasizing that even with having knowledge of the specific laws you're asking about related to gun storage, the answer to whether your dad would end up getting in trouble would be more based on probability than a 100% sure "yes or no" answer.
Also, the gun laws/requirements in my state have had a bunch of changes since the time that I went to that safety class (which was not that long of an amount of time in my opinion) and so there are new additional laws now or bills that have been passed and will go into law in another year.