Japanese allows for a lot of variation in terms of word order, as long as your particles are right, but it’s my impression that putting お母さんと before 学校に sounds more natural. Also, if it’s your mother you’re talking about, just using 母 would work as well, as you’d typically use お母さん when talking about someone else’s mother.
Also, I’m not sure if the ん at the end of 飲んで is a typo or not, for if you are going to use ん in the slang/informal context, it should usually be followed by any variation of です like “んです” or "んだ”
What I would write is: 普通は朝にコーヒーを飲んで、母と学校に行きます。
And as mentioned by the previous poster, I’d be careful about your choice of words in the title.