You’re right, he would have seen it. I reread the King’s Cross chap. last night. ON pg.719 it says “At last he knew what DD would have seen when he looked int the Mirror of E. and why DD had been so understanding.....So obviously he looked in the mirror and did find out who killed Ariana. The answer may have been hard for DD.
I took that as Dumbledore wanting to see his family alive and well, the same way Harry did.