It sounds to me as though your ex has wandered into the world of "we need to find these people something to do" in regard to retraining. This is the land where they want to put work requirements on all public assistance, and force everyone to have a job, when many times, the jobs just are not there and if they were, the people just aren't the quality of employee they need.
And if there are jobs available, they aren't well paying jobs that require a great deal of training. And people who already have bad backs, or other types of work restrictions are not the most in demand anyway. But we go on and provide training regardless. And those types of training IN NO WAY guarantee that you'll find a better or well paying job even after you've done what was asked of you and gone through the trainings.
Medical assistant (read nurse's aide) is a really hard demanding low-level job that first and foremost: 1.) makes it highly likely you'll hurt your back doing the everyday tasks required on this job and 2.) makes it real hard for you to find another position especially in the better (better paying) facilities once you HAVE any sort of record of back troubles or past back injuries. It appears your wife worked at this job after her first training for about five years. That's plenty of time to hurt your back badly, and as I said, it's almost an inevitable outcome of this type of job, certainly a daily hazard.
So yes, it is quite believable that she has had the training she's had and is still unable to find something. Medical coding jobs are like reindeer. They do exist, but really, only the eight who come out on Christmas really have a steady job. Lots of people would love to do medical coding jobs from home, mostly sitting down and the training sounds very attractive. But in reality, there are not many of these jobs, and it is not easy after the training to find a placement in the field.
In fact, in our area, the department of labor soon stopped paying for people to attend those kinds of training, as we were basically dumping training money down a black hole, where the people were paid minimum wage as long as they were in school training to do these jobs, but then when they were ready to go into private employment as a ....well, medical coding specialist for example, the promised jobs were not there. All six of them were already filled unless you wanted to load up and move your family to Bolivia to work (fluent knowledge of Spanish required).
So don't assume this all comes down to your ex-wife being a deadbeat co-parent. Don't be bitter or think you have been in some way taken advantage of. Kudos to you for having paid your child support, and I would bet from the sound of things she has struggled to keep things afloat even with your paying it regularly. Even if you don't like her, you've done right by your children and that's what counts.
Judges are very used to seeing very marginally employed people as both sets of parents, and will probably not think she's the special exceptional deadbeat mom unless she really acts out or speaks out inappropriately in court. They're much more likely to believe her story (they've seen and heard it all before so often) about how she has not been able to find much in the way of well paying jobs.
Please, do not waste your time worrying or be bitter about whether or not your ex wife has "done her part" or really done all she could've done not to need your child support or something. You have apparently moved on and I hope you do well, as well as your children who are now "aging out" of the need for your support.