so sorry to hear your news, I too asked the same question re my mum and the reply I got from mums GP was " there are no survivors of Alzheimers" only people who are battling it. A tough answer but it has made me appreciate that I am in effect dealing with a terminal illness and I totally understand your relief at mum being released from pain etc at the end of her illness.
remember to look after yourself very carefully and grieve without guilt.