Insert standard lawyer disclaimer that this isn't advice, y'all aren't my clients and I don't do criminal defense anyway, and further standard lawyer disclaimer that the law is messed up in all kinds of unpredictable ways, and here are my two cents:
The Delaware Supreme Court has said (in the Griffin v. State case from 2012) that because there is an express constitutional right to bear arms (Article I, Section 20 of the Delaware Constitution), the statute criminalizing concealed carry of a deadly weapon without a license (Section 1442 of title 11) is subject to a three-part test in particular cases. The court will look at (1) the strength of the state's interest in public safety against the individual's interest in carrying the weapon, (2) whether the individual could have carried the weapon in some reasonable alternative manner that didn't violate the statute, and (3) whether the individual was carrying the weapon for a lawful purpose.
Taking your gun to the range in a case, or putting it in your car in a case to take it to the range, seems like it ought to be an easy call on all three points, which is why the State Police don't camp out at Ommelanden arresting everyone who shows up without a CCDW card. The statute could have clearer exceptions, but putting those in creates the risk that we wind up with something like Maryland's statute -- there's a list of things you're allowed to have a gun in your car on the way to or from doing, but if you're not doing one of those (or you're planning to stop in at the range on your way home from work, etc.), then you're (potentially) in a world of hurt. More exceptions in the statute create more room for micro-management by the cops, if their bosses so order.
Ultimately, the answer to this is cultural. Getting pulled over with a gun in your car ought to be like getting pulled over with a set of jumper cables in your car. Cops who are normal and are respectful of the right to keep and bear arms aren't going to hassle normal people over ticky-tack garbage, and if they do, prosecutors who are normal are going to drop the case like a hot potato. Compared to certain nearby states I could name, Delaware cops and prosecutors are pretty normal and respectful of RKBA. Long may they so remain, and long may they be justified in so remaining.