How to start trusting after cheating

I am a mother of 2 young kids (both less than 2yr old). My husband cheated. Initially, i thought it were massages with special services only. Cried talking to him, he denied and said that i overthink, it was normal massages and if I m concerned, he shall not go anymore. However, within 1 week after our talk, I found that he still continue to search online for such services and lied about his whereabout. Recently, found out through his phone messages that he has been engaging prostitutes. I sat down to talk to him, he denied too, saying that he search/enquire for fun, its just enquiry, he never go.. but i saw everything including messages like location to meet, he has reached and the after review etc..when I told him what I have seen in phone, he tried to deny it but did not dare to show me the phone when i asked for it, and said that if i don't like, he shall not 'enquire' again, he said he still know his priority is still the family. I didn't want to keep arguing with him to get him admit as it feel it will go nowhere. To me, if he is willing to stop, I will let it go and move on. I know I am silly, but i also tell him that if for some reasons he just can't stop the desire to go, he should just be honest to me, i am prepared to consider some arrangment ie. Let him to go occasionally but he should try to limit the times, no emotional attachments and must practice safety measures to protect me & child. He said that he don't need such arrangement, he will just stop. Throughout the talk with him, he has never apologise to me, just deny and say he won't go or enquire again, his priority is still the family and that we should move on. It has been few days since the talk, now whenever he is using the phone, I got very worried, wonder if he still arranging to go. He has even changed the phone password as he knew i found out by checking his phone. How does couple gain back each other trusts after cheating? Should I be concerned that he changed his phone password? I also starting to doubt myself and whether he really still love me..or am I just someone to take care of his kids now.