If your choise line to invite Aunt to go together with Lil is blocked, have you tried to do what the game suggests to you?Ok. I give a key from my room to aunt. then she slept there for 1 day.
Next day she want to give the key back to me, i say 'no, take it yourself' and this day i go to sfamily with Lil and there is a screen but without possibility to press Invite.
for example the line before the menu:
"You need to talk to her about stepfamily, before you can reveal where you're going."