My mother will not ask my brother, me or my daughter to take her places. She will ask people in her neighbor before she asks us. I had a discussion with her not too long ago about this. I said it is almost like she has too much pride, that she shouldn't have to ask us - that we should you run over there and say 'okay, ready to go?' My sister-in-law told her that we cannot read her mind, if she needs something, she can ask us. But she won't. I'm sure other people are thinking that we don't do anything for her. She needed to go to the store last week. I don't have a car. I told her to call my daughter and set up a time that would be convenient for both of them, and then she would take her to the store. But no - 2 days later she called a lady down the street and asked her to take her. I was really irritated! Two years ago, she had 2 strokes. We when to the hospital every day, and went to her house everyday when she came home. She forever talks about how she did so much to help the grandkids when they were little. I told her last week, 'you did those things because someone ASKED you if you could do it." She had no comment. She will do anything she can to get away from asking us. We are all getting rather annoyed. Can elderly people have a chip on their shoulder and be too proud to ask their children and grandchildren for help?
And when she talks about helping with the gkids is it all complaints or is it just rehashing the last time in her life she felt useful?
As Jessie already said, make it a point to call her and mention you are going out to the hardware/grocery/xyz store and would she like you to pick anything up or would she like to come along for the ride.
Has your mother always been a bit passive/aggressive? Not calling you for help is one thing, but then complaining about all she did for your children seems unfair (if that is what she was doing.) If this is how she's always been then I suppose you have ways of coping with it.
I recall a conversation my mom and her sister has in their forties (my late teens). They were talking about getting old and incapacitated. Aunt said, "After all I'm doing for my kids, they certainly better take care of me in my old age!" My mother said, "If someone has to wipe my butt I don't want it to be one of my kids. I'd want someone who does that for a job." And decades later Mother really was content is a nursing home..
If your mom is more comfortable asking a neighbor for a ride than asking you, please don't take that personally. It is not your failure, no matter why she is doing this.
And the literal anwser to your last question is "of course they can!" Stop expecting her to be reasonable about this - it's not her style to do it your way, and you are just hitting your head on a wall trying to get her to change.