interpretation
Does

"If subsequent child development studies have shown that it is difficult for children to acquire fine motor skills until a certain age, diagnosing those who struggle thereafter as dyslexic or dyspraxic, I can only point them to samplers cross-stitched by average six- and seven-year-olds in the past."

mean

as child development studies indicate it is too difficult for little children to learn how to fix a complex motor, encountering those today suffering from dyslexia or dyspraxia, I only know the childhood compulsory sewing trainings the reason for such sufferings.

Question

interpretation
Does

"If subsequent child development studies have shown that it is difficult for children to acquire fine motor skills until a certain age, diagnosing those who struggle thereafter as dyslexic or dyspraxic, I can only point them to samplers cross-stitched by average six- and seven-year-olds in the past."

mean

as child development studies indicate it is too difficult for little children to learn how to fix a complex motor, encountering those today suffering from  dyslexia or dyspraxia, I only know the childhood compulsory sewing trainings the reason for such sufferings.

Answer

Fine motor skills aren't motor fixing skills! They mean motoric function, or motions done with your fingers, such as sewing, writing, drawing etc.

Perhaps they mean the samplers are evidence of early problems, but definitely not the reason. We might need to see more context.

Answer

This is quite technical, and as Marina said, needs more context to make good sense of.  It's a slightly strange way of phrasing but it might be OK in a wider context.  The "if" clause suggests that this is a hypothetical situation - the writer doesn't seem to know the results of the "subsequent studies" but is nevertheless speculating.