Prepositions rarely translate directly, and just as rarely have just one uniform meaning. There is no real reason other than that's simply the preposition that's used for this particular construction.
The simple explanation is that "tänker" means to think about something as in having it in your thoughts, "tycker" means to think about as in having an opinion.
But wouldn't "Hon tänker på hennes mamma." also be translated into English as "She is thinking about her mom."?
To me it seems like translating this sentence without specifying "her own mother" is leaving something out from the translation from Swedish to English.
Please correct me if I am mistaken or misunderstanding this,
This seems more about the ambiguity of the natural English sentence though, and saying 'her own' adds a particular emphasis that I don't think the Swedish version has (?)
Different languages carry different information, and sometimes you lose a bit when expressing the same idea in another language. That's just how it is, and "she's thinking of her mother" is the most natural way to express the idea of a woman thinking about her mum. If you need to prevent a possible ambiguity, then you need to start throwing in extra clarifying words to hammer the details home