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"After spending many grueling hours reseaching fathers being awarded primary custody, I found myself intrigued rather than bored."

You weren't bored before. You didn't understand what was happening. When you say bored, I picture you as callous, which I assume isn't the truth.

"With my background and desire to practice family law, coupled with an education from ______, "

The bit about your education is a throwaway. Get rid of that clause.

You definitely need to run this through spellcheck. Otherwise, I like it.

This is a sincere & convincing personal statement that clearly illustrates your interest in pursuing a legal career. The tone is appropriately professional.
The word "countless" may be the most misused word in the English language-- consider using "myriad" or "numerous" instead.