Yes, they do allow pets in Home Depot as long as they are kept under control.
Well, they didn't let me in with my rhinoceros,
Yes they do allow pets as longest keep them under control
Yes you can. As long as it's well behaved. A lot of people bring dogs into the store and there's also guide / service dog training that happens at the store. As far as the strangest animals I've seen brought into the store are African parrots and roosters. So I think you're safe, you'll get attention for sure either way.
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