Re: I don't want to hurt my wife but I'm not happy
OK, then roughneck, man up, tell the girl. She deserves to know. As for what you did and who you did it with, I am going to hazard a guess and say it isn't an ongoing thing with the same woman, but rather several instances with randoms, judging by your work rota.
You WILL have to live with the fallout, but if you genuinely feel bad about it, and REALLY don't want it to happen again, then stay away from situations where it could happen, stay off the drink, out of bars, and come straight home to her after every hitch away. Take the steps to ensure it won't happen and make sure she knows you are doing these things.
It isn't going to win her trust back, but it may be enough to convince her not to kick your ass to the kerb and take you for 60% of your **** and a hefty lump of your pay-cheque as well.