frankly, I think national reciprocity is a 10A violation unless we are talking about a national CCW for interstate truckers.
Either way, I don't picture certain states obeying it.

Individual states can have the option to elect to respect a federal issued permit. Any state may also have less restrictive requirements and issue its own in-state only permit. In my ideal, the federal permit would reflect the strictest requirements such that any state would accept it.

I believe states should be electing into a national UBC program and all states should be financially (federal $) supported to participate as Full point-of-contact in NICS.

Then it should be in a locked container secured to the vehicle. It certainly should not be left unsecured in plain sight.

I'm not a fan of home storage laws for several reasons. One, I don't think they are enforceable because the police don't get to search your home to ensure secure weapon storage. Two, I think they are redundant and will almost never be enforced. Prosecutors can already charge parents with negligent child endangerment if a child obtains an unsecured gun and shoots himself or someone else but almost never do because of the (presumed) emotional trauma the parent is undergoing as a result of the shooting.

Guns only belong in plain sight when in use and when for sale (supervised).

I have no interest in allowing law enforcement any random rights to "inspect" a home. However, if a gun is fired and a report is made, they likely have probable cause.

I'm okay with storage laws for homes because in the case where a child may find a gun and either, kill, injure or endanger a third party, the charge (for the gun owner) would be correct. While prosecutorial discretion should be respected, I suggest that not restraining folks from leaving their unsecured weapons accessible presents the same danger as not securing their swimming pools. Indeed, having a weapon easily accessible could be considered an 'attractive nuisance'.

I sympathize with parents that are overcome with emotional trauma after a child has injured or killed themselves or a sibling but it seems wise to bring them to trial. Such a parent has, IMHO, demonstrated their neglect, lack of wisdom and general recklessness. An authority should have at least the justification to step in and remove that parent's continued right to keep firearms at least so long as a minor resides with them.

When my children were young they went to a friend's party. Before dropping them off my wife called to ask if they had firearms or other weapons in the home. See was told that they did. On inquiring further it seemed safe as the rifle was locked up, the ammo was stored in a locked box and bolt opened and barrel locked with a cable lock.

Maybe your children are wise/mature enough, maybe what you're doing works for your family. Everyone should ask themselves, "Does what you're doing work for any young guests?"

and is largely already in place as the states voluntarily have begun to coalesce around a rather common set of rules and increasing cooperation entirely independent of the federal government. The federal government should never be encouraged to stick their honking camels nose under that tent.