I'd never sneak Alice in anywhere, but I'm very much a "rule follower" lol and I'd just be too nervous about getting caught. The only places she's gone into with me are pet stores and to pay the car insurance because an employee has her dogs laying around in there all the time and they like to see Alice.
I don't see a problem with a small dog being in a carrier or purse in a restaurant though, I'd do it if it was allowed
and wouldn't be bothered by someone alse doing it.