Only one person in the room needs to be 18+. I did this for our DD a few years ago. There were four teens in the room, she was 18, two were 16 and one was 17.
both of my kids have gone to WDW with friends for their graduations....agree with previous posters...one person in the room must be 18...and they do have to show id........when my kids went they did allow me to call the day of check in to put a credit card on the room so they could charge meals to their room keys
Just so you know: It's not Disney or DVC policy--it's FL law (or at least that's what they told me when my DS was 17 and I got stuck w/work...I was going to send him down in the morning and I'd join much later (late night or perhaps early the next morning)...Disney told me FL law would not allow them to let my DS check in...there was no way around it.
So, my "condolences" (grin) but yes, you will have to join your kids! Hope you have as much fun w/them as I've had w/my DS and his friends when we did a "kids' trip" for his graduation! (they were old enough to go w/out me then, but graciously allowed me to join in the fun (not to mention pay for their dinners!)