You need to trust your boyfriend... if he loves you nothing will change that. Concact w/ an ex in anyway shouldn't affect your relationship. I understant it is his family, but it's just that his family. My in-laws have let my hubby know that I am their daughter & even if something happens between us - I will still be a part of their lives. But I have also given them their 4 almost 5 grand babies.
For whatever reason the relationship between your man & this woman didn't work - so not matter what is on facebook, the problems that split them up are still there. Everyone has the right to be friends with who that want to be, you only have the right to choose who you will be friends with - not who anyone else will be friends with.
When I was expecting my 2 1/2 yr old - my hubby ran into his ex... she wanted to hang out & talk w/ him - I guess she was going through a hard time & she wanted someone from her past to help her through it. Eventhough it was hard & over the last 18 yrs (3 dating & 15 married) she has caused a lot of issues - I couldn't choose his friends. I did lay down "rules" - she isn't to come to my house (I pay the bills & the home loan is in my name only), she was not to be near the kids (they were to small to protect themselves at 2 & 3 1/2) and that I wanted nothing to do with her because I didn't trust her. He did follow the "rules" and only when to her - it didn't take long before she was paying her old games & he soon remembered why they when their own ways so many years ago. I never said anything to him about it - no "I told you so's" and if I would have tried stopping it... it would have just drove a wedge between us. In the end I still have my man - he knows I trust him & all in all it's another thing that brought us closer & made us a stronger couple.
Just keep loving your man & accept his families choose to be friends with this lady. Doesn't mean you have to be, in the end it will work out best for everyone!