My children would, I know, be appalled if I said that I wanted to end my life in order never to be a burden to them. They regard family life as being give and take - there are times when you are the giver, and others when you are the taker.
When I was ill earlier this year, they would offer to do things and I would say that I did not want to trouble them, at which point they would explode and list all the times I had helped them, not just as children, but being the recipient of their troubles and source of what they see as wise counsel and support. They clearly did not regard it as a burden, but just one aspect of life's rich pattern.
I had a difficult relationship with my mother, but did not see it as a burden to organise her care - it is just part of life. I got on very well with my Dad and was happy to organise his care, even though it was a huge challenge at the time. At no time did I regard it as a burden - hard work yes, but not a burden. They were my parents for goodness' sake.