Let's start with some basics. If you were both enrolled in a qualifying family HDHP all 12 months of the year, then you each have a personal contribution limit of $7300 (and an overall family limit of $7300), no matter whose name the plan was in.
If your employer paid money into your HSA and then removed from the HSA by your employer because you did not qualify for the matching funds, it should not be reported on your W-2. You need a corrected W-2. Otherwise, the IRS will view that you made a contribution that you did not. That may impact your ability to contribute other funds.
If your spouse had a cafeteria plan where funds were deducted from her paycheck pre-tax and deposited into the HSA, that should also be reflected in your spouse's W-2. They need a corrected W-2. (Technically what is happening is that employees agree to a salary reduction and the employer contributes the difference to the HSA, along with any matching funds. The box 12 code W amount should reflect the total of all contributions made by payroll plus any matching funds.)
No, it is not proper to report your spouse's payroll contributions as own contributions. When your spouse makes an HSA election, their salary is reduced which is reflected in their W-2 box 1 wages. To make the example very simple, if your spouse's salary is $50,000, and she elects a $3000 HSA contribution, and has no other salary adjustments, her box 1 wages would be $47,000. The HSA contribution is already subtracted from her taxable income. If you list it as a separate deduction, then you are taking credit twice, you are double dipping, subtracting money from her wages that was already subtracted from her wages by the employer.
