@htt Yeah, as a native English speaker, I can confidently say that English is confusing and weird. Thanks for your hard work!
"The nouns we use to talk about our families cause a lot of trouble. The rule of thumb is, when you use a word like mom, dad, or aunt, capitalize it only if the word is being used exactly as you would a name, as if you were addressing the person directly. If the word is not being used as a name, it is not capitalized—although that has nothing to do with the word’s importance."
Source:
https://www.grammarly.com/blog/proper-nouns/
So, "I gave my mom a flower," and, "I gave Mom a flower," both mean exactly the same thing, and both sentences use proper capitalization based on how "mom" is used. The same would apply for "baby;" without a preceding determiner, it becomes a name.