So, I was really bothered by how Future Claire found both Peters towards the start of the episode, as she didn't use Molly, and I find it hard to believe that in the whole of New York, she just happened to stumble on them
So I re-watched that little bit again, and I noticed something:

(that was the best pic I could find)
althought I put that off as being a regular person with formula-granted super speed, if you watch that bit again (the picture here isn't clear enough) the speedster has distinctive blonde hair and navy blue clothes- which were what Daphne was wearing when we first saw her
Therefore, when Daphne runs past both Peters (just as f_Peter is saying "With one big difference...") she must have spotted Peter, but didn't stop to confront because she is scared of Peter
She would then have gone to get Claire, and it's possible that Daphne can drag people along with her (so would have brought the Haitian and Claire to where she last saw Peter). Daphne would have left, claiming that Claire wouldn't really manage to kill Peter, and the Haitian and Claire would have gone looking for them
Claire finds Peter heading into the alley with the painting, and sends the Haitian round to the other side in ambush, before shooting f_Peter
Later, when Claire brings in the seemingly dead f_Peter, Daphne, although having previously claimed that Claire wouldn't manage to kill Peter, is surprised to find that Claire actually succeeds
I know this isn't too important, but I found a few people commenting on this plot-hole, so I decided that I would try and find an explanation