I have almost the opposite situation, although I have always tried to be independant. My daughter and one of my sons frequently take time off work to take me to hospital appointments, despite me saying I am happy to use hospital transport. They say they don't trust me to tell them the truth though I can't think why.
The problem is that they feel rather resemtful of their other two brothers who agree with me that I can make other arrangements. They do all turn up when there is a major emergency and all, including some of the grandchildren, lined the corridor at the hospital when I was going to the operating theatre for a triple by-pass. My difficulty is in letting the first two know how much I appreciate them whilst at the same time I do not feel any less for the other two, who have also been loving and helpful on other occasions.