Ordinarily I would write it off and not waste my time. I would feel uneasy about meeting Wednesday with girl potentially starting on Thursday. That doesn't give either or you much time to digest an interview and meeting.

However, in this case, maybe it really is a short notice move, in which case they would be rushed to get going. Although it seems more likely that it is stepdad's first time having to organize this and he really is unaware he needs to have put more time into this process. That is the only thing that would cause me to rethink meeting with them.

If you are considering going ahead, I would maybe email them again, see if you can narrow down their place of employment and hours, where they live exactly (can you search to find what school they would attend?), and see if they can meet sooner than Wednesday. Or even tell them that while you can meet Wednesday, you will not be able to start their child until Monday. That will give you a few days to think about it.