Caring for Aging Parents

Please can you give me your advice—-I am very troubled. Last December my mother became very ill with a stroke. It was a huge shock ans she is now in a nursing home after massive organization on my husband and my part. My father is 86 and wants to stay in the old family house . He will never be able to manage long term but has a cat and wants to stay put. He is almost harder to help than mum because he denies he needs help, then forgets whether he has eaten, whether he has taken his pills, and where he has put his wallet. I am divided between mum and dad, so much so that I actually feel sick with exhaustion and cannot even sleep. However, I love them and want to do all I can. My huge problem is my sister. She came out from New Zealand for three weeks at the start of all this, then basically packed her bags and went home because she couldn’t cope with it. She hardly saw mum and did nothing in dads’ house when she was there—he said she read a book. When she left, there were no meals cooked for him. no washing done, no cleaning. She did nothing. Because of this and her laziness and cold attitude, I had a lot of fights with her. I apologised as I didn’t want a rift and she said everything was fine. That was a month ago and she hasn’t phoned me —or mum—-since then. Her husband phones and says she doesn’t want to talk to me. And gets him to do all the asking. I wrote my sister a long e-mail saying there was no reason for her to be upset, she did a good job etc.   Even tho I don’t mean it, I sent it to calm any troubled waters. Her husband rang again and said my sister “will think about” whether she will answer me or not. She hasn’t.
I don’t know how to cope with her horrible ,self-centred attitude. How can I get it out of my head? I really can’t sleep because of her and I need to be rested as my parents are a full time commitment.  She shocks me deeply. Also, I have done all the hard, hard work and she wants to know all the details of mum’s home so she can ring and have the same respect at the home as I have—–and she has not only done nothing, but added to my grief and worry. Is this just my ego? Or am I right to feel so deeply hurt and angry about it all? What is your advice, please Deepak. Will you help me please?