During the academic year, plebes can leave the Yard on Saturday for a certain number of hours. This is not the same as being able to leave the area and be gone overnight (that's a "weekend" or "overnight") - plebes may earn some of those later, but certainly not at the critical weekend marking the transition from Plebe Summer into regular academic year companies. You are still executing PS training schedule at that point. Book/stuff issue, computer issue and set-up, mandatory training, getting ready for class start - it's a crazy transition time, and often plebes do not even get town liberty the Saturday of that weekend.
Getting permission to be away for important family events is hard enough, and for a plebe that particular weekend....well...it would be an unlikely exception.
This is where the reality of an active duty status, immersion military academy experience is the proverbial bucket of cold water on the head. A fact of life in the military is missing important family events because of duty requirements.
You can always ask, which means routing a special request chit through your chain of command. Setting a precedent will always be a decision element. If they let you go, what about other plebes who ask? PS experience is about everyone experiencing and embracing the suck together.
Now, here's a suggestion that I am not making in jest, because I know at least five mids who have done it. Faced with missing a wedding or other family event for military reasons, they ordered "flat daddies." Flat daddies are life-size photos on cardboard that stand up, which became and continue to be very popular with deployed military members, so as to be "present" in a humorous but visual way in photos or at events. Google flat daddy or party stand-up.
First things first - get the appointment, solve other problems as they present themselves.