"please tell me the numbers on lines 2-13,"
Sorry, I meant lines 2 through 13, not 2 and 13 - the curse of English.
"In regard to me being allocated a share of the Family HDHP limit, it was my understanding that by being covered by an HDHP plan, I could have opened my own HSA account and we could have shared the Family limit. "
Absolutely true.
"That is a bit different from what you are saying, that there is no such thing as a Family HSA account."
No, what I am saying is not at all different. Yes, the owner of the HSA can spend money for medical expenses for his/her spouse, any dependents, and even some people who are not dependents on the return but who would have been except for various reasons. This is why taxpayers often think of an HSA as a "joint HSA" because the couple can both contribute and be the recipient of HSA dollars.
But when the IRS says "Family", they are referring to the type of HDHP plan you have, because this determines your annual HSA contribution limit. That is, the concept of the higher contribution limit does not depend on the type of HSA (there is only one type), but on the type of HDHP coverage that you have at any given time. This means that the same HSA's limit may vary over time, as the HDHP coverage changes over time.
Your history makes perfect sense. The only thing you could have done differently (and most taxpayers don't realize this), is that you could have opened your own HSA at any time. Why would that matter? Because if you, the owner of the HSA, are 55 or over, you can increase your annual HSA contribution limit by $1,000 - but only to your HSA. If you two have two HSAs, then each of you can contribute that extra $1,000 - but each to his/her own separate HSA.
This is why you might see people talk about the annual HSA contribution limit being (this year) $9,200 - $7,200 for the Family coverage shared between the two of you, and 2 times $1,000...but you must put the $1,000 into the two separate HSAs. So the limit is actually $1,000 to one HSA and $8,200 to the other HSA, or you can split that $7,200 anyway you like.
As for what you want to do (changing the allocation of the Family limit for the prior year), TurboTax is following the direction in the instructions for form 8889. The wording of the instructions assume that the allocation was fixed when you filed your 2020 return. As you recall, when TurboTax detects a failure to maintain HDHP coverage, it calculates the HSA limit that you would have had had it not been for the last-month rule. Look at the last page in the instructions, which refers to the Line 3 Limitation Chart and Worksheet. The language here just refers to line numbers and does not make allowance for changing the allocation on the fly. Indeed, I would not have though that this would make a difference.
I will be honest that I had never thought about going back and amending the 2020 return to change the allocation to benefit the taxpayer who failed to maintain HDHP coverage. What I do know is that TurboTax does not allow this. You say that you have the desktop software and have tried to override the 8889 for both years, and TurboTax won't let you. In any case, to do it the right way, you would have to formally amend your 2020 return, then carry forward your 2020 data to your 2021 return (yes, that means start over on your 2021 return.). I am not sure that the reward is worth the hassle, but the choice is up to you.
To amend your 2020 return, please read this TurboTax Help page. This result of this process would have to be mailed to the IRS.
Then you would have to delete your 2021 return and start your 2021 TurboTax software again and re-import 2020 data to it.
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