No-win scenarios, relationship friction, duty and responsibility, increased pressure and ticking clocks, power struggles

The character disagreeing with a spouse's parenting decision
Having a significant other who doesn't get along with the character's family
Being a mid-level manager, caught between the workers and upper management
Being good friends with two people who were in a relationship but have broken up
Being a child of divorced parents who are always talking badly about each other
Playing peacemaker in a family feud
A political figure trying to meet the needs of people with opposing views
Being a confidant to two parties who are in conflict with one another
Loving (and investing in) a pastime that one's significant other hates
Being accountable to co-founders who have preferred ways of doing things
Being asked to keep a secret that really should be revealed
The character being asked for an opinion when they know the truth will upset the other person
Being blackmailed to do or say things that hurt someone else

Experiencing frustration or feelings of helplessness
Being pressured to take a side
Struggling to remain neutral
Awkward conversations and encounters
Feeling overlooked or voiceless
Lying by omission and telling half-truths to keep the peace
Being honest with a wrongdoer and being castigated for it
Being used by the involved parties (via a bid for power, to get back at each other, etc.)
Being pressured by one party for information about the other 
Having to reprimand an employee or co-worker
The character never feeling like they can be truly honest
Trying to please both parties and ending up pleasing no one