Should I trust my boyfriend of 10 years

been together 10 years .. we are in our late 40s.we had a lot of trouble with my daughter on drugs and we were fighting a lot.. He moved out for 3 months but was seeing a lady that works where he works lied to me about it.. but he said it was over and he came back I have adopted my grand daughter she is 4 and he has been with us for her whole life and she looks at him as daddy and was a mess with him gone after losing her mom and dad and her grand dad she thinks everyone is going to leave her... she is happy he is back her world is back in order.. But this is the kicker He went to the other lady's house today he doesn't know I know that... He was there for 1 hour he still has is apartment and goes there to get mail on sat... he left to go do that and went to her house first ..he has been back here for 6 weeks and this is the first time this has happened and he tells me he wants me to trust him.. I am keeping this to myself right now.. But it is killing me he tells me he loves me and he loves my grand daughter and has said to me if this doesn't work he knows I will not see him or let him see my grand daughter anymore... We love him very much and I hate this...I own my on home don't need him for help ... But I worry about my grand daughter if I make him leave... But I don't want to be lied to or used either.. He has said to me he couldn't ask for any thing more here....should I wait and see if he goes to her place again and then do something...And I know she has not been to his apartment .. I have a PI on this.. I don't know what to do I am keeping this to myself right now... but is driving me crazy... I called him on his cell phone he has thought I have been following him.. I said I called to let you know I am home he said you don't have to do that .. I said to him knowing he had just left her house... You want me to trust you and I want you to trust me he hesitated for a min and said OK... What would you do ???