Dear Lolly
You have taken a useful step by writing on this site.  Welcome!  I hope you will find the information and support that you need.
I think you are describing your inability to trust what your partner tells you and have turned to a bit of ‘detective work’ to check things.  A lot of us who have a partner or family member who gambles have done this, although it probably doesn’t feel good?  Lies and addiction go together – it can help to remember that as a sort of ‘fact’;  this might help lessen (at least a little) your sense of being betrayed and deceived. (Your partner is not intending to betray you, although of course his ‘secret’ actions are hurting you terribly.)
Perhaps it is a way of trying to get in control of the situation?  However, none of us can control the addiction or the person who has it.  I would suggest that an important step for you (for all partners and family members) is to begin to think of your own ***** as a priority, to recognize that you cannot control your partner or his addiction and to ‘persuade’ yourself that he is the one who ***** to take responsibility for the gambling.  This is not easy, but with support, good information and practice, you can get going on this journey.  Look after your own finances and make sure they are safe. 
It sounds like you are also fearful of bringing up the subject with your partner.  I think the important thing is not to get involved in arguments or to sound as if you are making accusations.  This would make your partner feel attacked, he will defend himself and no progress will be made.  Also lies are a big part of the addiction, as I have already written above.
Can you find some way of calmly explaining that you don’t yet feel ok or reassured about his problems with betting and that you still feel very concerned?  Can you also find a way of calmly telling him that you want to support him if he wants to get the right help to live free of gambling, but that you don’t want to have any part in keeping the addiction active?  It is NOT good to make an ultimatum of any kind unless you KNOW FOR SURE it is something you are already prepared to carry through.  (You may need such an approach at some stage, but no need to think that way yet – only if it becomes really necessary for YOU). 
I think I am suggesting that you try to speak calmly about your own feelings and avoid accusations and rows.  Then leave things in your partner’s court.  Give him telephone numbers or website details for getting help – eg Gamblers Anonymous, this site.  Try not to work out in advance how things should be;  take one step at a time, see how that works out and make decisions as you need to.  Most of all look after yourself, emotionally, practically and financially.
Keep in touch.
Very best wishes, MoniqueKeep hope alive.