Sounds to me like she needs some baby steps to address her own doubts and learn to deal with her parents. I would suggest a conversation something along these lines (obviously, change as appropriate for your relationship):
1. The deal is you are both happy, period. Reiterate that you will do whatever it takes for her to be happy, and that her just trudging along is not an acceptable solution. You will support whatever she decides.
2. This does not have to be an all-or-nothing situation. Who knows how much of the hatred of the former job was the job vs the people vs the hours? Maybe trying this one out part-time would help her address her concerns about not paying her share/earning her own money/etc. [this is where you reiterate that you are perfectly fine with her not bringing in a steady paycheck, but you see she is very worried about that and so are trying to brainstorm solutions.]
3. Since she loves training, what needs to be done to turn that into a career? Training, certifications, networking, etc.? What does she need to do to get going on making that happen? If this is going to be a business, can you help her develop a business plan to get there?
4. Maybe the part-time job is a good way to split the baby -- give her a steady paycheck so she feels like she is contributing, give her sufficient time away from the office to do what she needs to build her own side training business, and give her some breathing room to really plan how to grow the business slowly and steadily instead of feeling like she has to rush it to start bringing in a paycheck.
5. Nothing has to be permanent. If this job isn't right, she has your permission to quit at any time. Making the "wrong" decision here is not the end of the world.
6. You will handle her parents however she wants. It makes you batshit crazy when you see how they make her feel inferior if she doesn't follow their approved career path, and you hate to see her doubt herself after those discussions. But they are her parents, so she gets to decide how you deal with them - you are more than happy to tell them to step off, but if she would prefer you will hold your peace.
I think the sensitive stuff here is that training isn't something you can just snap your fingers and make any money at -- it is a business, and it needs to be planned and run like one, and even under the best circumstances it is not hugely remunerative. And, frankly, most people who have a passion for a side hustle spend a lot of time developing that passion in their spare time, while still working a full-time day job (the owner/lead trainer at my Crossfit gym, which has been around for @4 yrs, still runs out at 7 every morning to go work his day job!). Your wife is in an incredibly fortunate position to be able to focus on the training business while working only part-time, or not at all. I think it would help to lead her gently towards thinking of the business side of things, which involves a lot of planning and time, while still being supportive of whatever she ultimately decides.