In english, saying "Mom said (or any other verb)...." indeed implies that it is your mom. If you were talking about someone else's mom, you would say his mom / your mom / Bryan's mom, etc...
By your explanation, I take it that Italian is the same way. When you talk about Mom, it is implied that it is your own mother.
I think you only use "mamma" on its own if you are speaking directly: eg." ciao mamma." But you would ask a child, "dov'e la mamma". Even within a family, a father might say, "dov'e la mamma/la nonna" But, dov'e tuo fratello/tua sorella.
In English, generally speaking, we would say " Mum does not like my report" without "my", just to other family members. Otherwise, it would be "my mum" . My own aswer was rejected AGAIN, because I used the word "report" which we use in England, instead of "grade report". It has been reported to Duolingo, by others too, but it keeps coming up. Pazienza!
The verb "piacere" (as well as the verb "mancare") is difficult for English speakers because they can feel backwards to our thinking. Piacere means "to be pleasing" and the verb tense always has to agree with the thing that IS pleasing, not the person TO whom it is pleasing. The person to whom it is pleasing must be preceded by the preposition "a".
So yes, literally the sentence means "To mom, my report card is not pleasing". But no English speaker would say it like this, so the best translation in terms of meaning is "Mom doesn't like my grade report / report card."