Translation:My mother is shorter than me.
Huh? What's your point? The sentence was about the speaker and her(his?) mother. Bert never said you should use [母] when talking about somebody else's mother.
Also, I would appreciate it if you explained what you mean with saying that [母] is informal or casual. What would the non-casual or formal word for one's own mother be if [母] is a casual word?
If you're talking to your own family about your own family members: お母さん, お父さん, お姉さん（おねえさん）, お兄さん（おにいさん）, etc. If you're talking to other people about your own family members: 母（はは）, 父（ちち）, 姉（あね）, 兄（あに）, etc. If you're talking about other people's family members: お母さん, お父さん, お姉さん（おねえさん）, お兄さん（おにいさん）, etc.