I've done it twice and swore I'd never do it again. LOL!!
He won't go in a carrier, he throws up in the car, he barks loudly at other dogs, he pees in the aisles, I can't carry him with packages in my arms, he gets tangled in his harness, people want to (gasp) touch him, I'm afraid he's going to get stepped on and basically it's just not a fun experience for me.
I used to dread going to the mall with my two kids when they were really young. By the time we all got ready and the diaper bag packed I was to tired to go out. Nope I LOVE being able to shop without kids and dog in tow!
