I'd love to know whether Fiona was present at the doctor's appointment, because this is an incredibly important question. It could just be a huge (unfortunate) coincidence that they were trying to get leave for Fiona 2 days before she went missing, but unfortunately it could also indicate something a lot more sinister. Especially considering that this visit to the grandparent was supposed to be a 'surprise'. I'm sure LE are giving this all they've got, hopefully there's more going on behind the scenes than they're letting on.
The anonymous phone calls give me hope. If I've read correctly, and the two tips came from the same number, it may mean that Fiona is safe and well, and someone is hiding her for some reason (possible custody issues?). Especially considering the sightings were at the place that they were planning on travelling to (the reason they were trying to get Fiona out of school for 3 weeks).
Although, it could also be someone trying to throw LE off.
IMO and all that.
Where is this darling little girl?