I became unemployed in May 2016 and convinced my ex-wife to pick up my son (whom I am claiming as a dependent) on her health insurance while I remained covered all year by my own plan. He is shown on my 1095-B as only being covered part of the year, but was covered by my plan or her plan the whole year. I do not see unemployment as a qualifying hardship in the TurboTax guidance. Will I be penalized? How can I show he was coverage by a health plan for the whole year?
You should select "we all had health insurance all year" because your son was covered by health insurance all year, and according to your information, you were as well.
The Form 1095-B is not a required entry on the tax return, maintain this in your file with your other tax records. If you are questioned later you can get proof of insurance from the mother for your son. (see images attached)