A House Divided is available after completing Mankind Redefined. This quest makes for an entertaining exercise in conflict resolution. It turns out that a couple scientists aren't pleased with your quick inclusion in The Institute's ranks. Start by speaking to Newton Oberly in the Bioscience department. After talking to him, pick up the Bioscience Systems Access holotape and go past the door he just opened for you.
After taking on a couple Synths and turrets, you'll come across Lawrence Higgs (with a piece of glass in between you two), one of the scientists who doesn't like you. You can call this situation as a standoff, but Higgs doesn't know that you hold all the cards, specifically a holotape.
You can resolve this conflict one of two ways:
Use the nearby terminal to turn off the turrets and release a pair of Synth gorillas to maul the Synths and doctors.
Use the nearby terminal to open the door and then kill the Synths yourself while sparing Higgs and Loken, the other scientist. Loken will have the sense to end the standoff.
Choose the first option and Newton will be upset, but it won't affect your relationship with Father. Choose the second option and it'll be up to you to decide a punishment for Higgs and Loken.