Handedness is inherited, and there are several models that explain it. Here are some abstracts documenting it:
It's quite accepted that the brain has lateral specializations, and this translates to handedness as well. While handedness is a continuous variable and the brain is plastic, that is not to say that there is no dominant side to begin with. Much of the population are genetically right handed, some of it left-handed, and presumably a few with relative symmetry. This study cites another that came up with 8% of the sample of adult brains showing no asymmetry, with 82% left-biased and 10% right-biased:
http://www.sciencedirect.com/science/article/pii/002839329090032J (you'll probably only get access to the abstract)
The study goes on to describe morphological differences between the hemispheres - it's not simply that the two halves do different things, they have different sizes and connections for their component parts depending on the individual. Anyways, most people do have a dominant side, and while handedness and asymmetry are both continuous I think the number shows a good ground to conclude that most people do have a dominant side (even if we can't say all, but since you rarely can say all in science to begin with, it's not much of a point anyways).
A forced conversion of handedness can lead to anxiety and stress, which would explain a lot of the symptoms. It's similar to any other kind of parenting that runs counter to the child's disposition, leading to anxiety and stress. Prolonged anxiety can open up the possibility of developing mood or other psychological disorders. Anxiety and stress is pretty well known in psychology to cause anything negative you can think of - that is uncontested. If you learned to work with both hands in an organic way where anxiety and stress were not involved, then evidently plasticity did its thing.
The problem here isn't every vs. many, it's that parents don't understand it's a thing and when they try to hard to get what they want, very rarely will the child's mental health and development be appreciated. If you want to be super-strict, you could say handedness conversion isn't the root cause of those symptoms, but relentless anxiety and stress from the lack of validation, acceptance, self-esteem and so on resulting from said conversion.
I just finished my PSY100 exam and even though I don't have primary research, the topics were covered as having a general consensus in the psychological field. I'm not going to try and find the original papers for that - they probably go back several decades, if not a century. Psychology isn't the hardest science anyways, but a lot of the models proposed do have practical value in the form of developing new treatments and for that they're worth accepting. You can never prove something in psychology - due to our limited, though expanding, understanding of the brain as well as confounding through dealing with the human factor. But, you can supply evidence and a plausible mechanism in a that conforms to that evidence is all you need to create a useful model.