How does a caregiver get past the guilt of placing a parent in nursing home or assisted living?

My sister moved in with our mother 7 years ago and it was her plan to care for our mother up to her death. However, circumstances changed and my sister died August 2009 and my mother became incapable of being on her own about 4 years ago. I assumed responsibility for my sister both medical and financial in April 2009. In May she was diagnosed as terminal and was placed in a nursing home until she passed away. I spent time with her there almost daily. I was still working full time and caring for my husband and son. Then my aunt who was like a mother to me was diagnosed with pancreatic cancer September 2009 and given 4 months to live. Two weeks later my mother had a heart attack and it was determined she needed a quadruple bypass, she was 83. She had the surgery and recovered in rehab center. Her sister, my aunt died December 2009 just days after mom came home to my middle brother's house to be cared for until she could return to her own house. Less than 3 months later his wife ordered her to be moved back to her own house. Mom was good to live on her own by this time. However, she progressively failed in her ability to care for herself because it was not safe for her to try to cook her own meals. At this time I started to do more for her each week. Although I gathered my three brothers together in September 2010 to inform them that I was not emotionally strong enough to care for mother and the responsibility would fall to them. I was wiped out by the care for and loss of my sister, the major surgery for mom and her journey back, the loss of my aunt and then the brother who took mom in told me I could no longer see his two younger children whom I had babysit every week on my days off. These children were like grandchildren instead of niece and nephew and I went into depressed state. It took me months to get out of this condition and by this time it was increasingly obvious that mom was going to need a lot of assistance. Then an incident where mom fell and ended up in the hospital for a few days. The day after a major storm which knocked out all power and brought down trees around our houses, she needed to leave the hospital. My younger brother agreed to take her to his house for a few days. Four days later his wife told me to come get my mother that she was no longer welcome in her house. My mom had been intentionally peeing the bed, in the hallway and making messes for my sister-in-law to clean after. This was just spite on my mother's case. She does not like this sister-in-law. So two brothers with a home will no longer invite her in. The oldest son is dying of stomach cancer and can barely care for himself. Now my mom is becoming increasingly abrasive to me. She will not do things at her house that she is physically capable of doing. Picking up a tissue if she drops in the floor, not making coffee because she doesn't remember how, etc...the only time I get a break is when second brother is available to fix her breakfast or supper. This is not very often. My brothers do not help by driving her to any of her appointments, grocery shopping for her or even picking up any of her prescriptions. I have since retired in January 2013 thinking that maybe taking care of her would not be so difficult. That is not the case. I am now short with her, do not want to spend any quality time with her and although I have intentions to help her keep the house spotless she infuriates me so much with her attitude that I OWE her this that if I spend a total of 30 minutes at her house it is a miracle. Since I am not getting any assistance from my brothers I have told them I feel the time has come to consider putting her in assisted living. She is physically capable of caring for her hygiene, showering with minimal help, can still change remote to her favorite shows and does a little light housekeeping and dishes. However, it is hard for me to make the decision alone and carry out with moving her out of her house.