What is the best way to resolve conflict (constant arguing) when living with elderly who have health problems?

Out of our depth: This is a big question and is not a simple one to answer. My initial thoughts are asking your family doctor for any community programs that would provide adult day health...A day care for the elderly to lessen the burden on the caregiver. Also i wonder about other mental health programs and therapy around the burdens of aging and providing care. The last option is one that includes nursing home.

Stressful situation.: Caring for an unhealthy elderly person is very stressful, and can easily make you more prone to outbursts of anger and intolerance. There are support groups for caregivers, and nursing homes often offer respite care where they watch your elderly relative for a week or so to give you a breather. That may break the anger cycle you're in.