I dont know what to do

My OH has a kid with his ex-gf. Ive never cared about them talking or anything like that until she found out about me years ago. When that happened her texts went from only about their kid to things that had nothing to do about their kid. She had just gotten married when she met me and thats when she started flirting with my OH and he was letting her but he wasn't flirting back. I had told him i wasn't comfortable with that and he either needs to say something or i will leave the relationship because i didn't want to wonder if he was flirting back when i wasnt around. So it stopped for awhile and then last year i had seen on his phone messages again of them being friendly and asked him about it. Then all the sudden she became very nasty to him telling him he is a horrible father so again the friendly messages stopped. Now it's started up again and i know for a fact he just lied to me about something. Its nothing about him flirting back or anything but what they had talked about yesterday does not match what he is telling me today. In the beginning i had always seen the texts messages between them just because i was next to him when she would text him. After the first time of seeing her inappropriate messages he gave me permission to look at the texts any time i wanted but i never did because I thought he had stopped it. The second time i again was next to him and saw some texts from her i found a little inappropriate so i looked at his messages with his permission and he was present and i told him i really didnt like what i had found because some of the stuff he was saying could be taken like he was flirting back. Now this time my phone had not been working for a few days and was using his phone to get ahold of my parents and thats when i saw the texts. I didn't say anything about it but now that i know he lied to me im really on edge.

Side note he had gone through my phone before any of the above happened and saw texts messages with one of my guys friends that he didnt like so i stopped talking to the guy out of respect for our relationship. I was not flirting with my friend but my OH thought he was flirting with me and trying to be with me. Also i really dont feel good about them talking about anything other than their kid and her flirting with my OH because she has been caught cheating on her husband and she had cheated on my OH with her husband. I also just found out recently she cheated on her fiance she had before my OH with my OH. I also know she is only flirting with my OH with no intention of being with him because she hates him. She just does it to be disrespectful to me and my relationship with my OH. What im most upset with is i know my OH doesnt even want her in his life because she is a horrible person to him but he is not putting a stop or even trying to stop what she is doing. Because of that im starting to loose trust for my OH.