The person she's becoming is someone who seems to have a free-floating envy of the life of ease that Elly whines about. Elly doesn't realize it and chooses to gloss over it when she tells her but it annoys Connie somewhat that she had to go through all the trouble she did in order to finally find Greg and she feels that Elly should be more appreciative of being as lucky as she is. She's also somewhat annoyed that Elly seems to have such easy-going children who don't see her as some sort of tyrant and she's especially annoyed that Elly had a child late in life while either she or Greg are pretty much infertile.
The problem, of course, is that Elly doesn't understand that Connie is envious in the first place and wouldn't understand why even if she did admit to it. Doing so, you see, would mean that the people who tell her evil lies about how wonderful her life actually is are right and that would lead to her being wrong about things and that would lead to everyone from First Grade jetting on down to Milboring to tease her and call her names and would thus be terrible.