Hi!
The story you are looking for is called "Misunderstanding" by Jetbstraub is was posted on HP Fandom, but it is not there anymore. Maybe you could aks her, where you can find the story now.
If she can´t help send me a message I have the story on my computer.
There is also another story on HP Fandom called "You Bet" by Crimson Pheonix it´s a nice oneshot with the same threesome.