Are mixed handed or ambidextrous children more likely to have mental health, language and scholastic problems?
There is at least one study that has been done in a peer reviewed (and therefore presumably reputable) journal that indicates that mixed handed children do in fact have more problems of the sorts you mention than children who have one dominant hand. This result was shown in a study of children in Finland that tested them when they were 7 or 8 years old and again 8 years later.
According to the study's authors, the mechanism whereby these problems happen is unclear. Scientists do not know enough about handedness to be able to know for sure why mixed handed children would have more problems. The difference was, however, statistically significant and it manifested itself in particularly in that mixed handed children were about twice as likely to have ADHD as other children.
More about this study can be found in the psychcentral.com link below.
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