@ChristinaS18 -
I may not have followed your question, but I just checked by creating a calendar assignment for a group in a course, and only the student group I assigned the assignment to can see it in their calendar feed.
I don't go through the calendar assignment creation process normally, so I tried it out.
if I click on a calendar square and select assignment, I can enter the title and select which assignment group to put it in and then select more options(Note, I would make sure the calendar feed you are viewing is for the course you want the assignment in only)
Under more options, make it a group assignment, and select the group set then in the assign to area, get rid of everyone and select the group to assign it to out of the group set. Put in the dates and you are done. only those students in the group can see it on the calendar
Link to the instructors guide
Instructor page on add an assignment from the calendar
The calendar page is short and then redirects you to the edit the assignment details wiki
which then has a link to making a group assignment.
Let us know if you still have questions - or if I am off base with what I think you are asking.
Ron