Can someone tell me or point me in the right direction in what the quest title is that chooses sides (or last quest to complete before choosing sides).
Make sense? Sounds kind of confusing to me.
You can do all the quests up to the point they ask you to destroy the Railroad or fight the BoS/Institute.
You will also see a Pop-Up, which says, "You are now enemies with X faction"
There is a point where you have to grab a nuclear core for a reactor in the Institute. At that point, you will become hostile to either the Brotherhood or the Institute, depending on how you act and it will warn you either way. Becoming hostile toward the Railroad occurs after construction of Liberty Prime, where you choose to either storm them and take them out and then its off to the Institute.
You can pretty much advance the Institute questline up to "Nuclear Family" achieve, without stepping on anyone's toes.
There isn't any single quest tbh. There are several quests and events that make you hostile to other factions.
Don't worry, you will know when you get to the point where you become hostile to a faction.
You get Nuclear Family Achievement once you destroyed both the Railroad and the BoS so it is not really without stepping on anyone's toes...