"My wife should be able to contribute the difference ($5,104.17) to her account."
That's incorrect. She did not have family coverage the entire year. You allocated all of the prorated amount for family coverage to your contribution, so I calculate wife's maximum contribution for the remainder of the year with self-only coverage as:
$3,850 * 7 / 12 + $1,000 = $3,245.83. (rounds to $3,246)
Because she is over age 55 and was covered the entire year, she gets the full $1,000 catch-up. This still doesn't quite agree with TurboTax saying that there is an excess contribution of $2,118. Perhaps you entered something differently than you described.
