When is it Necessary to Spill the Beans?

I want to know when it becomes necessary to tell it all in a relationship. I am married and we have had our uups and downs. Towards the end of last year, my hubby was moved to another town. He lived alone for a month before me and the kids joined him. One morning he left for work and left his phone on the charger, he didnt turn off the phone. A text message came through and i picked the phone only to find that the text was from a female who wrote and i quote"MORNING WHAT I WANTD 2 SAT LAST NYT WAS THAT I M SORRY IF I MAY VE OVER REACTED. I THANK U 4 U VE TAUGHT A LESSON ND 4 UR OPENESS.ONE NIT THATS IT. THE LUST OF SEX WITHOUT MEANING . U SAID WE WILL REMAIN FRIENDS WHY DONT U PICK MY CALLS. WORK WELL FRIEND". After reading this i was devasted and i asked him who the woman was, but he told me that she was not important and that i should not be bothered to try and know whom she was. insisted the only thing he told me was that they met at a golf club and that she does not play golf. My husband plays golf too. I asked him to stay away from playing golf, he agreed and stayed off golf for a month after which he came to me pleading that he was used after working through the week during weekends he feels good playing golf, and that he would keep a distance from the lady. Unfortunately i fell for his plea and allowed him. Meanwhile i kept a close check of his phones. i discovered that there was a regular number calling him especially when he was working out of town. I investigated the same number and it was the same lady who had texed him sametime back. The problem was that all the calls where being made at night after 10pm.lasting 4 to 5mins, i got curious and asked him whose number it was and why the calls were being made at night. By the way i didnt mention the carreer of my husband, he is a medical doctor. so he told me that the person had a sick child and was calling to find out what could be done. But i asked there were 5 to 6 calls everyday calling almost at the same time. One of the his nieces even told me that one day she was in the vehicle with them. They looked happy talking together. Then i took the trouble to find out who the person was by going to the golf club house myself and i discovered that she was a golf secretary for their club and that she is a regular member there.
I was devasted to discover this and all what i am wondering is what does this man think of me, where does he place me in his life. After i discovered i asked why he has been hiding the details of the woman when he tells me that there was nothing between them. Then he tells me that there are something i should not know. I need to know what your opinion on the matter is. I am contemplating should i just leave him or i stay. when do people tell it all........