Should Emotional Support Animals be granted legal public access?

I have just started the process of getting an emotional support animal. My cousin also has a dog who she calls an emotional support animal. She has admitted to not seeking professional, psychiatric care for the issues she needs an ESA for. She just bought a vest online and takes her dog everywhere and anywhere. She's angry because at the store, the manager told her ESA's are not permitted in stores. This is true information. ESA's are not granted full public access by law. The ADA states that ESA's do not have the level of training to just be allowed wherever their handler goes. Also, it risks distracting a service dog and preventing them from doing their jobs. So what do you all think?