The biggest challenge of living with a resentful or angry person is to keep from becoming one yourself. The high contagion and reactivity of resentment and anger are likely to make you into someone you are not.
The second biggest challenge, should you decide to stay in a relationship with a resentful or angry person, is getting him or her to change. Likely to obstruct any attempt are your partner's:
Victim Identity Breeds Entitlement
Resentful and angry people see themselves as merely reacting to an unfair world. They often feel offended by what they perceive as a general insensitivity to their "needs." As a result, they're likely to feel attacked by any attempt to point out ways in which they might be unfair. They show little concern for the negative effects of their behavior on others.
Driven by high standards of what they should receive from others and what other people should do for them, the angry and resentful frequently feel disappointed and offended, which, in turn, causes more entitlement. It seems only fair, from their perspectives, that they get compensation for their constant frustrations. Special consideration seems like so little to ask! Here's the logic:
"It's so hard being me, I shouldn't have to do the dishes, too!"
"I'm the exploited man; you have to cook my dinner!"
"I'm the oppressed woman; you have to support me!"
Habit of Blame
Most problem anger – that which makes us act against our best interests - is powered by the habit of blaming uncomfortable emotional states on others. The resentful and angry have conditioned themselves to pin the cause of their emotional states on someone else, thereby becoming powerless to self-regulate. Instead, they rely on the adrenaline-driven energy and confidence that goes with resentment and anger, in the same way that many of us are conditioned to take a cup of coffee first thing in the morning.
The law of blame is that it eventually goes to the closest person. Your resentful or angry partner is likely to blame you for the problems of the relationship - if not life in general - and, therefore, will not be highly motivated to change.
I have had hundreds of clients who were misdiagnosed by their partners' therapists or self-help books with Narcissistic Personality Disorder. Although it is unethical and foolhardy for professionals to diagnose someone they have not examined, it is an easy mistake to make with those who are chronically resentful or angry. Indeed, everyone is narcissistic while angry or resentful. In the adrenalin rush of even low-grade anger, everyone feels entitled and more important than those who have stimulated their anger. Everyone has a false sense of confidence (if not arrogance), is motivated to manipulate, and is incapable of empathy, while angry or resentful.
Automatic Negative Attributions
States of anger and resentment feature narrow and rigid thinking that amplify and magnify only the negative aspects of a behavior or situation. The tendency of the angry and resentful to attribute malevolence, incompetence, or inadequacy to those who disagree with them makes negotiation extremely difficult. We're all likely to devalue those who incur our resentment or anger. Even if we do it in our heads, without expressing it, the negativity will almost certainly be communicated in a close relationship.
Getting Your Partner to Change
Due to all of the above, resentful and angry people will perceive any attempt to change them as manipulation, if not abuse. Chronic resentment and anger are degenerative conditions in that the reactions they invoke in others tend to worsen them. Their emotional range and subsequent world-view grow narrower and more rigid when they need to become broader and more flexible. Without intensive intervention, the only hope for changing the course of the disease is to wait painfully for some life-changing event, such as a near-death experience, a sincere religious conversion, or loss of a loved one.
Given that attempts to get your partner to change are likely to make things worse, it's imperative to focus on your own healing and wellbeing. Not incidentally, that is also the most compassionate thing you can do for your partner.