Friends with the Married Ex - When she asks if you two would work?

My boyfriend told me early in our relationship that he still in is contact with his HS sweetheart who is married with three kids….said they were friends….said that she asked him a little over a year ago (while married with 3 kids) if they would ever workout and he told her no. So she responded “ok just friends then”. I was uneasy about this but decided it was a really good thing he choose to tell me and I decided to focus on that. A few months past and we started to get to more of a serious relationship and I noticed this was very frequent texting with pics being exchanged. So I did something that I admit was wrong….I read the texts. I will admit they both did their best to not cross an imaginary line…..BUT they sent selfies back and forth, he told her how good she looked the last time he saw her, she kept getting whiney when he didn’t give her enough attention, she likes almost every single Facebook post he has, and she kept really questioning his and my relationship. The final straw was that he met up with her and her husband while out of town….while he was very worried that her husband be there and be ok….he not only didn’t tell me – he lied when I asked if he saw her. I know you are all going to say he couldn’t tell me because I’d overreact….but I promise this was all before I had a really big issue with this relationship. I think if her husband knew she wanted to know if their relationship would ever work he wouldn’t be ok with it either. I believe my boyfriend when he says he doesn’t want her…..but it just doesn’t sit well with me…..should it??