Yes, and beyond this, I don't get why "I drew my mom and dad" isn't a good translation. I've come thru too many sentences where the possessive pronoun is implied and then I get to this chapter, and suddenly the implication stops for no apparent reason.
Probably just an oversight.
However, this sentence says "We drew", so the most logical option is "our" (added now). However, it's not like "my" seems wrong. It seems like a reasonable interpretation that "we" are a child and a nanny, or a child and a grandparent, or a child and a teacher or any other configuration where two people were drawing, but the parents 'belonged' to only one. While if the child says that, "mamę i tatę" still makes perfect sense, there's absolutely no need to add "moją mamę i mojego tatę". So added "my" as well.