marriage question

how do i get my trust for my husband since he has cheated.when he leaves he dont want to tell me were hes going and if he does i dont believe what hes telling me.he tells me ever once and a while if he stays out all night long that he got stuck in mudd or to drunk to drive.i told him the next time he stayed out all night he would have to move out.no all of a sudden twice this week he had to take an out of town trip with a friend of his.i asked him why do they wait so late to go and his responce was because they have to work in the day so they leave almost mid night.and iam really supose to believe this.iam trying to wait and see if real proof comes up but it makes me feel like iam constantly diggin and waiting for something to hapend.i dont trust him but i dont want to push him into cheating again