Yes if you are going to use the term physician which is sort of correct but not what we would usually say - we would usually say doctor's unless we specifically mean a specialist paediatrician (these along with all medical doctors can be called physicians) in which case we would say paediatrician's, in any case we would say they are at the professional's practice or premises or surgery or clinic - hence the possessive apostrophe. The sentence is a shortened version as common when describing people's places: I'm at Jack's, I'm at the florist's, I'm at the Smiths' or I'm at the butcher's.
COPIL (singular indefinite) - COPII (plural indefinite)
COPILUL (singular definite) - COPIII (plural definite)
The subject usually uses the definite article if it has no determiner (adjective, etc.) or if the determiner is placed after the subject:
- Copiii sunt la doctor. Copiii lor sunt la doctor. Copiii bolnavi sunt la doctor.
If the determiner is placed in front of the subject, then the definite article goes on the determiner and the subject remains without an article.
- Ai lor copii sunt la doctor. Bolnavii copii sunt la doctor.
Of course physician was the only solution in this question, but if there would be a doctor template, I think all of us would select "doctor"! Physician offer such a large possibility that nobody would send their children to a physician without knowing about what he works.
but technically all medical practitioners are physicians so it has a general meaning as well, though i agree you are likely to say they are at the paediatrician's or at the doctor's or at the GP's in the UK or at the family physician perhaps in the states (I'm not American but am a physician!)