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.