I live somewhat rurally and when it was just Hot Rod, I took him everywhere. I only ever got asked to leave Target--and not so very nicely either. I didn't/don't have a problem being asked to leave, but they were very rude. I was only in the $1.00 section of the front of the store and the security guard yelled across the store. I asked if I could pay for what I had in the cart as I really needed 1 of the items that I had in the cart and he begrudginly said okay and then the cashier was just as nasty in telling me that I needed to leave. I told her that I was already asked to leave and that they said it was okay to pay for my items and she would not stop saying that I had to leave. If I didn't need this one item, I would have probably told her off saying that the sooner she stopped lecturing me and cashed me out, the sooner I would be leaving!!!
Other than that, Hot Rod was/is welcomed everywhere else we've been. I did sneak him in his carrier into the grocery store to pick up a prescription and all the cashiers wanted me to take him out and they even yelled out to the customer service people to come over to see him.
2 managers of 2 different Tuesday Morning stores say that hethey are always welcome in thier stores. One of the Joann's stores has 1 employee who does not like them other than that, everyone else loves it when I bring them in.
I would not mind if someone asked me to leave a store that I was not supposed to be in--especially if I did not know I wasn't supposed to be their, but it can be done nicely.