Only chain I know of that is anti-gun across the board, has reported guests to the police no less, are Trump properties. Really.
Most hotel chains are really vague about it because they don't want to get in the middle of all this. I mostly do Marriott because of loyalty programs (used to travel near 100% of the time), and have never seen a no-gun sign, or heard anything else about it. Nor, however, do I ask or tell. Never had a problem, even when carrying pretty gun-shaped cases, or cardboard boxes that say Mossberg on the side.
Lots of folks carry all sorts off stuff for work. Rolling in with a gun case means nothing to anyone at a hotel. Could be anything. Pelican cases especially are just cases. No one cares. No one will notice.
Do not let people see you. Unless absolutely required (some big city ones) do not use the main entrance, but a side door. Front desk staff pay attention to you for providing good service; a nosy one could conceivably wonder what all you are carrying in. Never seen it, but I can imagine. Also, always further to go. Park near a side entrance, use that. Avoid elevators if you can as well.
Motels? Seriously? Maybe way back when they were common, but now motels are leftovers. Cheap, junky, poorly maintained, poorly managed. You can break into them by looking at them hard, no amenities, etc. And parking spots are not assigned per room; very often you cannot park right in front of your room even if you get a ground floor spot, so cannot have proximity anyway.