In the following questions, fill in the blanks with the appropriate phrase.
The correct sentence can be re-written as:
Who will look after the children when their mother is in the hospital?
Look after means to take care of someone or something.
Look for: to hope to get something that you want or need.
Look up:Â (of a situation) to improve.
Look about: to try to locate someone or something.
Hence, Option A is correct.