I guess I don't see the big deal here...
You may initiate more, but she actively participates & does get in contact with you periodically. Some people are just not huge into other people's kids, some are embarrassed of their homes, or don't like to entertain, or may be too broke to entertain. Some get busy or stressed, or life sucks & they're not good at communicating with friends. I don't see where she's using or taking advantage of you, or mistreating you. I do see 2 people with different levels of neediness & expectations.
It seems like you are analyzing everything she does (or doesn't) do & making it out to be more than it probably is. Maybe you are looking for reasons to end the friendship, and these are the best you could come up with. IMO, it sounds like you both might be better of without each other, as it sounds you both have very ideas of what a friendship is. I know I wouldn't appreciate a friend keeping tabs & having expectations of me, personally, and you aren't happy with how she's handling the friendship. At the end of the day, you have to do what feels right to you.