First, what is your plan for safely storing your shotgun when at your girlfriend's if there is no safe and 4 kids? Do you plan to take it in and out of the truck everyday? Sounds like a big pain when an 870 express and a stack on gun cabinet is not all that much money. Neither are "top of the line" but both are adequate and much cheaper than a lawyer if you get yourself in hot water. It seems more like justification for a course of action that appeals to you than a really good solution or idea.
I think your assumption that you will be OK in MD is a big one, and given the anti-gun nature of the state not a risk I would really want to take. For instance what is, or is there a legal statement in MD code as to what "transport" means? does it mean I keep this gun in a case in my vehicle at all times? Note it says transport and not possession, some states refer to posession of firearms in a vehicle... whole other story. Or does it mean you MAY place a gun, in a case and drive it somewhere? See the argument an attorney could make here? You are not "transporting" that involves a start / stop, origin and destination, with some perhaps legitimate use of the gun, or need for the gun at one end or the other. instead one could argue you are carrying --- that is a state of always having the gun in the car, and that is not legal, or could be argued to not be legal or is not the intent of the law's discussion of transport. The fact you are here and elsewhere discussing it as always being there would not help you.
Again unless the word is defined by statute it's going to end up in court IF they want it to, which with the wrong set of luck it could well, then you have to write the big check to an attorney and slug it out in court. Odds are good that you would win, but do you want to bet on it and foot the bill?
You seem to be open to change as you have changed your concept of this considerably from when you started the thread and that's great as you are considering things. I would suggest that you continue to think it through as there are lots of other alternatives in all of this that are likely easier in the political climate you have to live in. Again so far as I am concerned it should be a non issue across the 50 states, but then we know that's a long way off.