I don't know if he's just an outdoor dog or what, but he's having a heckuva time walking on the kitchen tile and hard wood floors.
Probably has carpet in his home.
I've never owned a dog as an adult, but if my mom had found a dog, she would have dropped all plans and looked *in that neighborhood* for the owner. Since the dog was in a parking lot, she would have stayed in that parking lot, with the dog (she owned dogs so she always had an extra leash and collar in her car, at least until the last place she lived when she decided she was tired of dealing with the death that you have to deal with when you have animals), trying to find the owner. She would have talked to the store owners or mall management, letting them know THAT evening that a dog had been found, so if the panicked owners showed up they would know that the dog wasn't in the road somewhere.
So to me, taking the dog back to your home wasn't the most fabulous idea, but then I've been the home-front "wait for the dog" person while my mom was out for HOURS, in the pouring rain, at night, searching on foot for our aging dog who had somehow gotten out of our locked, very tall fence, back yard. I know what it's like to lose a dog (and a cat, sadly, when hubby didn't check for her when he was dealing with his dad's hospitalization...we never did find her) and to look frantically, all holiday plans forgotten entirely, and surely would have appreciated it if the finders had stayed in the area.
It's hard, your first holiday, after losing your mom. I remember that well. And I had all through spring and summer to get ready for it; it's so soon for you.
Just don't get too used to that dog, b/c I'm sure the owners are desperate to find it!