So I was thinking about something, and beyond the visual clues I think I have a headcanon that strongly suggests that Pinkie and Applejack are related.
Okay, so Pinkie notices that Great Auntie Applesauce is a fourth cousin Twice removed to the Pie family (or so she says). Now, even though the entry is smudged, Pinkie confidence suggests that the exact name of the pony that Applesauce is related to is one that Pinkie recognizes, possibly one of her parents or grandparents. When she reads this, she assumes that it refers to HER parent/grandparent. THIS is why she's initially so certain, before Applejack brings doubt into things by noting that what Pinkie subconsciously/automatically thought was "Pie" wasn't really legible.
Of course, this means that popular to what might be popular headcanon, Pinkie and Applejack aren't possible 4th cousins twice removed, but potentially either fifth cousins thrice removed, sixth cousins twice removed, or sixth cousins once removed. This is assuming either one or two generations between the unknown Pie, two generations between the great aunt (not up for debate by definition) and Applejack, and either side having more generations crammed between the common ancestor of the Pie/Apple family.
Yay for overthinking cartoon ancestry! Of course the best part of about this headcanon is that it doesn't conflict with canon because Applejack's doubts over where it says "Pie" are reasonable as ponies do seem to be capable of sharing "first" names with each other. Therefore Pinkie could still have jumped to the wrong conclusion just because she saw her mother/father/grandmother/grandfather's first name and mistook it as referring to said pony.
