@loveonlymeh15, if I am understanding you correctly, then sort of. If someone in your household buys a vet clinic, then they will be able to run the clinic (and I think any adult in that same household can run the clinic/be the vet.) But when you go to work and come home is up to you. It is a lot like owning a retail store in Get to Work, as you decide the hours you want your Sim to work. 😉 They will be responsible for fixing broke items, or restoking the vending machine that holds pet treats and medicine, as well as seeing patients and treating them.
So, if I understand your case, you want one Sim to buy the clinic and their son to be the vet at that clinic? 🤔 I think that might work if the son is an adult and lives in the same household as the Sim who purchased the clinic. I'm not 100% sure since I usually have whoever I want to be the vet be the one to buy the clinic, but I did have a husband and wife own and operate one when Cats & Dogs was first released. I think they both could run the clinic an see patients. 🙂