OK, I am going to look at this from a slightly different perspective from other posters, some of whom are being really harsh toward your wife (maybe deserved, maybe not...we don't have enough information to know.)
It sounds like there are three big things going on here:
1. Your wife came into the marriage without strong financial planning or management skills and has not developed them since (not knowing her loan amounts, not remembering how you have allocated money toward debt, poorly planned credit card spending.)
2. The two of you don't communicate well about financial decisions. We don't know who contributes how to that situation, but clearly you have trouble getting on the same page (wife doesn't feel she can tell you about spending, wife went ahead with certificate despite your doubts, you are not on the same page about MA)
3. Your long-term goals aren't in alignment. She dreams of education in something that fulfills her soul and hopefully the ability to make money doing it, and you dream of what? FIRE? You haven't really said.
Also, the tone you are using to talk about this is pretty negative toward your wife. Of course, this is a safe space to talk about something that has clearly been bothering you for awhile, which may explain the tone, but if you look at the research of Dr. John Gottman, who has a very high record of success telling which marriages will survive, he says that contempt toward a partner is a big predictor of an unsuccessful marriage. Maybe it's totally deserved (again, we just don't know from our perspective) but I take it you would like to stay in the marriage since you are asking for negotiation/persuasion techniques, not the address of a divorce attorney.
I mean, you could tell the exact same story from a whole different point of view, like this:
Dear Mustachians--I hope you can give me advice on handling a delicate situation with my amazing wife. She has many wonderful talents, but she struggles with financial planning and management. When we got married, she wasn't even sure how much she owed in students loans, and she doesn't always recall accurately what financial decisions we have made together. She doesn't always spend within our means, which has been stressful. Our communication dynamic around finances isn't great either...there have been times when she didn't feel she could tell me about credit-card spending. Still, she was there for me during the stresses of law school even through her own first pregnancy (did I get that math right?)and has stayed out of the workplace to raise our two kids, even though having two little ones at home is pretty tough, at the same time doing the household chores and supporting me emotionally during the early years of my new career. Three years ago, once I was making decent money and our younger was getting ready to go to elementary school, she wanted to get more education and contribute financially to our household. She found a certificate program in fine arts, which really spoke to her, and completed the program for less than the cost of two years of community college (based on my local community college's student costs). I'm really proud of how hard she worked after being away from an academic setting over 10 years. The problem is that there aren't many money earning opportunities with this certificate, but she's really excited about this field and now wants a graduate degree which would be very expensive and probably require us to move just as I'm settled in this career. Plus, I'd really like to pursue my dreams of early retirement (yes? no?) and her fulfilling her dreams will make that tough. How can we get on the same page over these issues?
Maybe your wife really is as bad as some of the other posters think, none of the above applies, and all you can achieve is crisis management. But is there any way to look at the situation more kindly, which will probably help negotiations move along better?
And as others have pointed out...given the communication challenges, maybe a good counselor could help you find a more successful way of negotiating 1-3?