What are two examples of Amanda being an ironic character?
To answer your question about Amanda being ironic:
She is an icon that represents the stranded, stagnant, and quite unconventional Old South.
Amanda was strategically given characteristics that go hand in hand with her way of mind, and mannerisms: They conform to the dynamics of the US South its paradigms.
For example: Amanda is the typical Southern belle, expecting the "Gentlemen Callers", dressing up all pompous and over-working to over-entertain for a quite casual afternoon with Jim. She also has the Southern habit of embellishing her tales, repeating old stories, and being a charmer, hence, her Southern Hospitality.
In addition to that, she expects the same for her daughter, and is oblivious to the needs of his son, all for the sake of keeping up with the preoccupations that in another time and place would have mattered when she was younger.
Amanda is also preocupied with appeareances, and the need to keep them. Even though Mr. Wingfield had left the family in the most miserable manner, she still managed to stay firm to the tradition and had his pictured displayed huge in the living room. She also takes great pride on her pedigree, making comments about the grandiosity of her days in the South, and somehow always managing to remain there, in her mind.
What is IRONIC about all this is that she is living in a different time and place, where industrialism is drowning workers everywhere, where there is an economic depression going on, where her son and daughter are lost in cluelessness, and in a place where none of her actions would be considered typical in a fast-moving, dynamic city.
Imagine how ridiculous or strange her demeanor looked in front of Jim when she was being so extremely hospitable, witty, and exceedingly charming. She was also awkwardly over-dressed, and she had pre-planned way too much for a casual meeting. Jim, being a city guy, probably thought of this as the doings of an "odd old lady" and probably felt very weird in the process as well.
I don't see much irony in Amanda. Her position in the small family is clear, and her choices are limited. Amanda is a worried mother who has long ago been abandoned by her husband and left to raise two children by herself. She is worried about her older son, Tom, because she knows that he is not happy living in their little apartment. She knows he wants nothing more than to escape. This frightens Amanda greatly because of her other child, Laura. Laura is a shy and nervous girl, the kind of person who, her mother fears, will never be able to take care of herself. Thus Amanda's whole goal is to find a man for Laura so that when Tom is gone and she is dead, at least Laura will be taken care of.
So, Amanda's entire quest is to find someone for Laura... a gentleman caller who will come, fall deeply in love with Laura, whisk her away, and live happily ever after. This dream of Amanda's is highly unrealistic and ultimately damaging and the source of great disappointment, but there's no irony in Amanda, just an abject desperation that engenders impracticable expectations.
Now, of course, as Amanda incessantly tells the story of her youth to her children, she relates a tale of wealth and privilege and boys who were all competing for her favors and attention. If all of her stories were true, there would be great irony in relation to her present situation of poverty and abandonment. But, sadly, there's no way to know if any of that was real.
Amanda in Tennessee Williams' play "The Glass Menagerie" is the mother of Tom and Laura. Laura is very shy and walks with a limp. Her mother engages her in schooling as a typist. She believes that Laura has been attending and she stops to check in on her. She finds out that Laura had checked in one day and left shortly after starting the school.
Amanda can not accept reality. Laura is mentally unstable and yet her mother constantly pushes her towards being someone she can not be. One of the ironies is that she sets up a date for Laura with a friend Tom invites to dinner. He is just coming to dinner but Amanda turns it into a date.
Amanda even stuffs Laura's bra so that she will not look like a gay receiver. Amanda shows up all dressed up playing the southern belle. She tells the man Jim about her former suitors.
Amanda keeps pushing Laura to like Jim and engage in flirtation with Jim. It is only at the end that she finds out that he is really married which dashes her plans for Laura to marry him. She also finds out that her son is not as close friends with Jim as she had thought. The other irony is that she calls her son Tom selfish when he devotes his time and income in the household.