Hi Paul,
If you were wrong I think she would laugh at you and not huff. Like if I asked you were you robbing a bank rather than playing golf? It seems like she is evading the issue and evading you right now as she does not want to face your questions.
However she does sound lonely although guilt induction is a very common tactic. Golf is a very time consuming hobby.
It’s not the frequency of visits which really indicates if there is a problem. It’s the amount of recklessness I would say . Also she may well have visited every time you played golf and not told you . Does she still have lots of new clothes, buy good food etc. I think living from paycheck to paycheck is a big red flag .
It strikes me that rather than seeking help you immediately see this may be the end of your 31 year long marriage so perhaps there are other issues here and maybe both of you would benefit from exploring these . Although it could be of course that this issue has worried you for a long time and you are only able to confront it right now .
Here is a link to gamanon, a website for families of people with a gambling addiction. You may find the questions here useful.
http://gamanon.org.uk/?page_id=32
I hope you find that your wife is not suffering from a gambling addiction Paul.