Confused since husband said its not cheating

I'm very confused right now so please bare with me as im dealing with some health issues. Husband and I have been married for 21 years. He was an alcoholic for 19 years of marriage. He has been sober now for a couple years. Due to his drinking in the past i have alot of resentment since i held down the fork here with our kids. Anyway he picked up jiu-jitsu he started helping coach. Sometimes everyday.There is another girl there that helps coach as well. Last year he bought her a gift and started communicating with her alot more on social media which made me feel uncomfortable. I told him keep it straight about jiu-jitsu. Well i had a feeling that he got alot closer and didn't respect my boundaries. So i went through his phone. They had been sharing Instagram memes up to 5 times a day. And started communicating on there about his childhood and her past marriages and her current marriage. Not sure at what point they got close I felt betrayed cause he didn't respect my boundaries. I also know her so i was hurt. I confronted him when i seen she had send him something on Instagram that morning. He deleted her after we fought to keep the peace according to him.He still thinks he didn't do anything wrong. I feel like its emotional cheating am i wrong? Its fucked up cause here i am supporting his hobbies so he can stay sober. I mean supporting as im the one worrying about our own kids and he does this. I still have her on social media. Should i delete her? He's supposed to get his family in order but has time for this. How i barely have time to text a friend back.
If everything here at home was ok i wouldn't be so resentmentful but its not. I waited for him for so long.