Her time is important too. Old habits die hard, certain types of people get into habits of being predictably late. I'm late by 10-15 minutes for almost everything, but it is a consistent lateness. It takes a lot to break habits like that.
My advice would be to accept the perceived flaws in other people, like your mother and appreciate the time you do spend together.
You might miss those quirks about her when she is gone.
I can see what you're saying but it is very important to keep agreements. If you and I were to agree to show up at 2 and I show up at 2 but you show up at 2:15 that is simply not fair as I have gone out of my way to take the effort to be on time. Being on time definitely is an effort.