I suffer from anxiety disorder/depression myself. I take high doses of meds and still go to therapy. I've been through two layoffs. It was Not Pretty. My dear husband was a rock and incredibly patient. He is a real mensch, and I feel lucky to have him. We are BOTH frugal though, so we've had very little disagreements on money and were able to structure our finances where we could withstand some punishment to our cash flow. I have also worked in a couple of toxic work environments, which played merry hell on my psyche and gave me a bad case of burnout, contributing to the anxiety disorder (one of these jobs involved an hour's commute on a very nasty stretch of highway).
In short, I sympathize with your wife. Mostly, not entirely.
The bitch about anxiety disorder is that the sufferer is not operating in anything resembling "normal" reality. The disorder can also sneak up on you where you don't always realize how far you've sunk. I still fight my issues regularly, and my main improvement from therapy has been learning to step back and TRY to be more objective about the situation at hand. This is far easier said than done. Anxiety disorder also keeps one ALWAYS on the defensive, sometimes assuming bad intentions that are not there. Keep this in mind. Her world is not your world at this time. If she gets panic attacks and the like, then she probably feels very much not in control of things already.
In the worst depths of my anxiety disorder, I was afraid my husband would leave me, find someone who wasn't so much "trouble." Maybe a younger woman, too, while he was at it (I'm five years older than he is). That was the pesky neurotransmitter imbalance talking. In truth, my Sweetie still makes goo-goo eyes at me five years in.
Let's look at the timeline here, and try to walk in her (perhaps overpriced) shoes. How long was your wife at the job she quit, before she married you? Did her commute from that old job improve or become worse upon moving in together? Do you know if she was helping out her family then?
So far:
3.5 years ago you had a shotgun wedding.
3 years ago your son was born.
2 years ago you turned over a new leaf, financially. Your wife did not buy in. (Where, exactly, have you saved up that 100K? Is it even in joint accounts?)
1 year ago she quit FT work, with your blessing, once her anxiety disorder got the better of her. Did you make job search expectations clear before you gave your blessing? Did you work on a budget then?
She spent some months unemployed, then got her part time gig a few months ago (but just quit it?).
From her point of view I imagine it's something like this: A few years back she had a decent job, her own place, bought whatever fun/shiny things she wanted, and was doing all right. Some job stress, sure, but who doesn't have it? A little bit of a credit card bill run up, but don't most people? (not my view, just sayin') Being in her early thirties at the time you met, she's used to having a lot of autonomy. Then she meets a guy, and has an unexpected pregnancy. From an anxiety perspective that's a huge OH SHIT right there. She moves in with her soon-to-be-spouse, is now accountable to another person, has the baby, has to juggle the baby with her stressful job, keeps buying unnecessary things for a quick mood fix, and has a little breakdown.
Perhaps she was dealing with a bit of post-partum depression at the time, too? How far/how close does her family live to you? What's her local support network like? There is a higher likelihood of PPD if a new mother lives far away from family and friends' support.
In any case, you are being seen as "the big meanie" who doesn't offer her a bit of your cash to subsidize her normal (and reasonable, to her) expenditures even when she is busting ass keeping everything together. I don't actually agree with this view, mind you!
She's probably feeling very insecure. In that mental state it is also hard to take a long term view. But she has to WANT to help herself as well.
Try framing her actions in terms of giving her security: "I am doing this to make sure OUR CHILD has a good, stable life and good education. I'm doing this so NEITHER of us have to work a crappy job that drives us insane, but buys us time to find a decent gig. I want to make sure that WE are not eating cat food in retirement, or losing the house in a layoff. I need YOUR HELP in this goal by doing/not doing x,y,z. If we continue on this rate of saving, we will reach FI in XX years, IF YOU HELP US get there. I know you are stressed out right now and I want to HELP YOU deal with it in a productive manner. We can get through this."
Does she like the field for which she was trained? Would some retraining help if she bought into it? Do you suspect any crisis of confidence on the career front?
Remember- this is the mother of your child. If you go for the escape hatch, you still have to deal with her for oh, 15 years yet. Consider the cost of divorce and child support vs. going a little slower on the savings rate. Hell, bribe her for reaching milestones if you must! Also remember that in 2-3 years the kiddo will be in school and she will have less pressure on her time and sanity. Is she afraid to put the kiddo in day care? Ask her to plan for the short term to intermediate future. Again, she is very much on the defensive already. Show her that you are really on HER side, not her adversary. Show her that she is actually in a safe place (which might not happen without therapy/meds/both). Don't smack her on the head with a rolled up newspaper like she's an errant puppy.
I agree with the sentiments that she needs professional help. I hope she is willing to find it. She also needs to work on boundary issues with her family. It sounds like maybe money=love in her mind. Given how your relationship started, there really wasn't time to establish family boundaries before the mega-stress hit; try to bear that in mind. That gets very complicated very quickly. But she is a big girl and her first responsibility is to her husband and child.
Good luck. I can only imagine the sort of stress you both must be under right now.