I would get a bad vibe from family #1 by now. Communication and trust are VITAL to a healthy working relationship and these people haven't even responded to your email. That is pretty rude and not a good sign. I am sure they are checking their email at least once a day.

Perhaps they are buying more time while they interview others. I think that someone really serious would have made contact with you within 24 hours and said they were bringing the deposit before your space fills up.

I would be setting my sights on family 2 at this point

Good luck