Let me see if I can make it understandable:
1) This person was born a woman in Hawaii.
2) She decided not to be a woman anymore and officially became transgendered. So, she is now a he.
3) Problem — She/he took male hormones but did not take her female organs out.
4) She/he married a woman. The marriage is recognized in Hawaii.
5) The woman could not bear children.
6) He/She decides to bear the children by insemination because his/her female organs are still intact.
7) He/she succeeds and bears 3 kids which he/she and his/her partner raise.
8) They move to Arizona (where only one man one woman marriage is legally recognized ).
9) After 9 years of marriage he/she wants a divorce but can’t get it because Arizona does not recognize the Hawaiian marriage in the first place.
I guess the only solution is for him/her to go back to Hawaii to get the divorce.
You are correct, it is neither, since she no longer lives in HI and is not and never was a man.