@abasket I understand your worry, and I guess it is dog dependent. As far as HD, I believe most allow dogs in the store, so maybe your husband could take the dog in with him?
My 2 loved to just sit in the car; they never left the backseat; one would sit up and watch what was going on, the other went to sleep. These were 45 and 55lb doodles, so not little guys that someone could grab and run. While doors were locked and child safety locks on the rear doors, it doesn’t mean someone couldn’t open the door with effort and take them; but again, the smaller one looked scary with his loud bark and teeth showing. I know I wouldn’t go near him if I didn’t know him while he was barking! 
The only time he didn’t bark at strangers was at home as I think he wasn’t threatened in his safe space. He was afraid of his own shadow; his bark was out of fear.
I think we only traveled with each dog once. We took the older one with us when my husband had a meeting in Nashville and stayed at the Loews Vanderbilt. They roll out the red carpet for dogs! While hubby was at his meeting, the dog and I wondered the campus and parks. The younger one stayed at a high in hotel in DC where my daughter’s work had a deal as it was around the corner from her office. Again, they provided a dog bed, bowls, bedtime treats, and toys. I wish all hotels were this accommodating.