The type of HDHP coverage that your wife had is a function of whether or not she was alone on that HDHP policy or if someone else (you or a dependent) was on the policy as well. "Family" to the IRS means "Self" plus at least one other person, no matter what the insurance company calls it.
But this is not something just get to select at tax time - you have to confirm with her HDHP provider (or her benefits coordinator) what kind of HDHP policy she had.
Based on your description, it sounds like you entered your information correctly.
The issue is that the annual HSA contribution limit in her case is pro-rated by the number of months she was under the HDHP coverage. If she had Self coverage and is under 55, then the limit is $3,400 times 6 months divided by 12 months, or $1,700. Any amount that she contributed over $1,700 would be an excess contribution that would be added to line 21 on the 1040 as Other Income.
You may have another situation: if your wife took advantage of the "last-month" rule in 2016, then she was required to stay in the HDHP for all of 2017. Clearly she didn't.
The last-month rule means that if you have HDHP coverage on December 1 (of 2016, in this case), she could contribute based on the full annual limit, not based on the number of months. Suppose she started the HSA in July 2016. She could have contributed the full $3,400 in 2016 because she was covered on 12/1/2016.
However, since she did not stay under HDHP coverage for the "testing" period (i.e., all of 2017), she has "failure to maintain HDHP coverage" and will be penalized for overcontributing in 2016. I am thinking that this is also part of your $1,000 change in tax, because the change due to overcontributing in 2017 because of leaving HDHP coverage doesn't seem large enough to cause that number.
