"At" might be the most difficult preposition. It has countless uses. Unlike most other prepositions (like "on", "under", "in", "outside",...) it has no obvious physical interpretation. In many ways, it acts more like an adjective than a preposition. It is similar to the adjective "near", but it is stronger, meaning "very, very, very near". Interestingly, "near" can function both as an adjective and a preposition, so the words are like cousins. I use "at" in a manner similar to pointing my finger at something. Saying "at a pet store" is like pointing "at" a pet store, saying its name, giving its address, or showing it on a map. So, "at" is more general than "in" which actually places you inside of a building. Your phrases work with either preposition.

You generally work in a store, at a company, and get something done at a store. The prepositions used for a situation evolve through use and are easily learned from experience. That’s how all native speakers learn them.

Here's a way to rationalize it in the context of a case-based language like Russian: ‘At’ can be thought of as being roughly equivalent to ‘у’ where ‘у’ is used with the genetive case and has to do with proximity to the thing's ‘territory.’ ‘Лечение зубов у Индиго.’ The service (dental care) is happening/offered at the place of Indigo. ‘Dental care at (the place of) Indigo.’ Also, dental care is a service, which is an abstract noun, so I would say generally, abstract nouns or services will more likely be used with ‘at.’ ‘Oil changes at Speedy Auto.’ ‘Tax services at ABC Bookkeeping.’ ‘Fun and relaxation at Greentree Resort.’ Another case: ‘I am at the doctor’ has the meaning of ‘I am at (the place of the) doctor's. Я у врача. To use ‘in,’ analogous to prepositional case, we would normally specify the exact place: ‘I am in the doctor's office.’ я в кабинете врача. Other times, ‘in’ and ‘at’ can be more or less interchangeable, but ‘in’ more precisely specifies that you are inside of a building. ‘I am in the store’ or I am at the store’ can both be used. But, ‘in’ specifies that you are physically inside the building whereas ‘at’ can be thought of as ‘at the place of the store’ or ‘at the territory of the store.’ In some US regions, people will sometimes unnecessarily use the possessive/genetive case for stores. Aldi and Kroger are two grocery chains, and some people will say ‘I'm at Kroger's’ or ‘I'm at Aldi's.’ This is a genetive, possessive type situation, where it has the meaning of ‘I'm at Kroger's place or Aldi's place.’ More generally people will just say ‘I'm at Kroger or I'm at Aldi’ or they may just use ‘in.’

because "care" is a noun work in the care at