Is 妈妈 considered a childish way to say mom?
Like how mommy is a childish word in English. For example if I️ want to ask someone in casual conversation "is your mom home?" would it be pretty normal to say "ni mama zai jia ma?" or would I️ say something else?

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Answer

媽媽 means mum, not mummy, and is the normal way to refer to your mother. 
母親 means mother, and is a more formal way to refer to one's mother
媽咪 is mummy, and is usually only said by kids.

Answer

As people get older it is more common for them to call their mother 妈 instead of 妈妈 however both are acceptable regardless of age and it would just be a personal preference.