"it assumes she has no insurance" TurboTax doesn't assume. You tell TurboTax in the HDHP section the kind of HDHP coverage your spouse had. If your spouse was covered by the family HDHP plan the entire year and had no disqualifying coverage, that's what you need to enter for your spouse's coverage.
Your spouse's HSA contribution must be made to your spouse's HSA, not to your HSA.
