Multi year ammendments with large refunds

I have recently discovered that due to a court order, I have been able to claim my children since my divorce, yet have never done so.  This goes back 8 years; but I'm only amending the last 3.  These credits add up! The question is - if I'm using TurboTax and bring up my taxes for each year, do I simply amend each year individually - or do I need to  amend 2016, wait for refund, import that accepted return into TurboTax 2017, then amend 2017, wait for refund, import that into 2018, then amend 2018, etc.

 

OR - can I simply amend each year as filed (bring up filed taxes, add claims for the children, print amendment)?  Will I be hit this next year with taxes on this "income"?

 

Seems complex if I need to amend last three years based on previous years amended taxes when trying to file all 3 years amendments at same time. 

Hope the above makes sense...