many times the 的 will be left off if their is a close relation or relationship. For example you don't need to say 她是我的太太。(she is my wife). Though you can, but many times people will just drop the 的 in that situation. 她是我太太。

Really, that "的" before "父母" is totally not needed. The "的" placement isn't even the same for other sentences such as “我和我朋友的关系很好” , which doesn't have the "的" in front of the noun

Is an answer with 跟 instead of 和 acceptable? I got marked wrong for this.

The 的 being omitted should also be accepted if the purpose of this course is to impart a native-like parlance.