Is it a valid reason for the mother to convert to Judaism “to see what the Jewish religion is like because the child wants to be Jewish, i.e. for the sake of the child” or would such conversion be deemed invalid?
When someone converts to Judaism, it is because the person has a deep belief in G-d, and because he wants to keep all of the commandments that G-d gave the Jews, including the rabbinical enactments . Without this requisite, the conversion is not valid. From what you are describing, it sounds like the parent does not have any real interest in being Jewish, but only because the child wants to be Jewish. A person can not convert if they aren’t totally committed to being a torah observant Jew.