In the HSA interview (Federal->Deductions & Credits->Medical->HSA MSA Contributions), you are asked what your HDHP coverage is: Self or Family. It sounds like that although you meant to click on Family, you must have clicked on Self.
On the screen with the heading "Was [name] covered by a High Deductible Health Plan (HDHP) in 2017?" (see screenshot below), you should have answered that you had HDHP coverage at least one month in 2017. Then three new lines would appear below, and on the first line, you should have indicated that you had Family coverage every month of the year (assuming you did).
TurboTax does not care what your filing status is - this has no effect on your HDHP coverage.
Another thought is that you had $3,350 in excess contributions carried over from 2016. This excess contribution carryover (if any) is counted as a personal contribution in 2017, and can cause an excess in 2017, if you don't reduce your other contributions accordingly.
The amount could have been carried over by TurboTax automatically if you did 2016 with TurboTax, or you could have entered it when TurboTax asked you if you "overfunded" the HSA in 2016. Note that if you had an excess contribution in 2016 but withdrew the entire amount before the due date of the return, then you do not enter anything for the overfunding. Why? Because by withdrawing the excess, you "cured" the excess and don't have to report it in 2017.
Why don't we (well, you) delete all your HSA information and start over? Please do the following:
1. make a copy of your W-2(s) (if you don't have the paper copies)
2. delete your W-2(s) (use the garbage can icon next to the W-2(s) on the Income screen
3. go to View (at the top), choose Forms, and select the desired form. Note the Delete Form button at the bottom of the screen.
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3. go to Tax Tools (on the left), and navigate to Tools->Delete a form
4. delete form(s) 1099-SA (if one), 8889-T, and 8889-S (if one)
5. go back and re-add your W-2(s), preferably adding them manually
6. go back and redo the entire HSA interview.