She was grown up enough to run off and have an affair now she can put her big girl panties on and be in the same radius as you and SO.  Why is BF letting her control the situation? It's not her choice whether you attend skids events with BF or not. H#ll, you could go alone to support skids and she has literally no say in it.  

If you really want to go just show up with BF, neither of you need her permission.  If he really wants to keep you he needs to stop letting drama mama control the scene.  

There is no reason for a formal "meet and greet" between parents and their ex's SO. Unless there is a legitimate, founded concern that the SO is hurting the kid, a parent just has to trust, or at least accept, that their ex is making good choices with who they bring around their kids. They really have no say in the matter.

Now, that ALSO means than an ex doesn't get to veto the parent's new SO at public events. Little Timmy has a recital and new GF wants to come? Great - she should go, be darned how BM feels about it (ESPECIALLY if BM is the one who ended the relationship). Dad has to realize that IF he is going to move on, he has to move on the whole way. He can't pretend to not have an SO to make BM feel better. Well, he can, but that is a sure-fire way to end a relationship.

BM will dictate EVERYTHING in his life so long as he allows it. He needs to feel pain from YOU, too, when he doesn't listen. Too often, new SPs sit back and let the crazy train run them over because society has beat into them that "the first family" is most important and anyone new coming in should just roll right along with it. That's hogwash. If your SO is putting BM's feelings before yours, then make it ABUNDANTLY clear how not okay that, up to and including ending this relationship. No one likes to think that this would cause a break up, but these little acts cause deep resentment years and years later. Snip it in the bud STAT.

If your SO is in any way excluding you from public events that, say, a grandparent or sibling would be invited to, tell him that you won't be excluded again. If he is celebrating holidays with BM and the kids but excluding you, tell him never again. His marriage and family with her is OVER. If he wants to move on, he does so 100%. Bringing the kids with him does not mean he brings along the ex, and if he can't figure out how to do that, he needs to get himself some counseling or more time single to figure it out.

It doesn't help the kids to play happy family. Kids need to see that romantic relationships can end, new and good ones can be forged, and that adults can work through conflict to accomplish a goal. What they don't need is their parents acting out as a "family". The kids know they aren't together, and it will either confuse them or teach them unhealthy, codependent relationship dynamics. Conflict, separation, disagreements, mutual respect, heartbreak - all these things are a part of life, and parenta have to teach their kids how to handle it and help ease the pain, not coddle to the point where no pain exists. It does a disservice to kids in the long run, and really is only a mechanism to assuage parental guilt in the now. Pretending to be a happy family with an ex is selfish behavior on behalf of the parent - parents don't do it to help their kids, only to help themselves.

So, start standing up for yourself and your place with your SO. You are the makings of his new family and his equal, so don't bow down just because it makes his life easier. You are the person he is choosing to spend his life with and to introduce his children to. Do not let him hide you in the background because he doesnt want to face the harsh reality that he and his ex couldn't make a marriage work. He'll never, ever move forward if he doesnt feel the full blast of his marriage ending and grieve the loss (past, present, and future) entirely. So long as you coddle him and he coddles BM and his kids, he will always live for his first family and put you second. And You will eventually get tired of being the second wife versus THE wife.

What kind of events are you talking about?  Kid's sports games or something?  If the event is occuring in a public place both your SO and his EX can bring whoever they want.  Neither spouse is obligated to meet or hang out with the new partners.. and vice versa.  As the GF, you do not have to meet her either.  I know that many people want to meet the other person and in some cases there is this thought that everyone can be adults and be civil etc.. for the sake of the kids.  Well, that rarely works out that way... I mean, I have been to some events where my DH's EX was.. and my DH speaks to his wife's BF of 15 years... but we never sat together or socialized.  It's not necessary.  I think arm's length is just fine and let the Bio parents be the ones that deal with their EX.

You should just go. In general, I would avoid a relationship with BM, however. Like ESMOD said, More often than not, it doesn't work out that the new spouses get along well with the birth parents.

So I would approach it as, you and your SO are going to attend sporting events, etc, as a couple, and if it happens that you meet BM, fine. If not, also fine. Just do your thing and don't let it control you and SO's life. BM doesn't get a say in any of this.

Do your own thing. They are neither friend nor family. 

So.... your man's BM insists on talking to him several times a day about innocuous things, taking up so much of his post-marriage life, but doesn't want to meet you. She had an affair... which I believe means she was with your SO and the man she cheated with simultaniously for a period of time. If I were to make assessments....

She had an affair because there were some things she didn't like about her husband, but didn't completely leave because there were things that made her want to stay. Since he wasn't the one who cheated, and he was devastated, he had strong feelings that don't just drop right away when he met the next person. Since they "have to" talk because of the kids, it's got to be hard dealing with the emotions left over from the whole thing. So they talk and talk and talk for any reason at all since they still have an unhealthy attachment. Therefore, I think they're still emotionally involved, still into each other, and the real reason she doesnt' want to meet you is because she doesn't want to think of you as "real." If she meets you, there you'll be, the symbol of her previous life officially moving on, in the flesh.

If she doesn't want to meet you, fine. But you are now involved in your SO's world, which includes his kids, and it's wonderful you want to go to his kid's events to show your support. So go to the events. If he tells you no in order to "protect" her from meeting you (makes NO sense), then tell him these words: "you are actively putting me second to this woman. This makes me feel like you still have feelings for her and hope to get back together with her. Are you moving forward with me by your side or not? If so, get your shoes on and let's go." 

The issue is called... control.  BM wants it.  By  influencing your SO and  you she is gaining some sense of control.

As for SO meeting  the guy his X cheated with....     ..... he shoulld go ahead and meet him.

I met my adulterous cavern crotched whore of an XW's primary adultery partner once.  My XILs had invited me to a garden party at their home.  They wanted me to remain part of the family.  This was before I relocated to finish engineering school.

 After we were introduced we were both at the bar grabbing a beer... I leaned over asked him how my D--k tasted.  He choked on his beer.  Apparently he never said a word to my XW about it as she never called haging out on me over it.

The ultimate revenge was 3+ years later when my XW wanted to sell the home we purchased together 3mos before she moved out. We did a lease purchase of the home to a single mom before I moved.  A year later my XW moved back in to the home because she didn't like how the lady who was executing the lease/purchase of the property was interfacing with her. 

She wanted me to quit claim deed it to her for $10 (Texas requires monitary exchange for any real estate transaction) so that she could sell it.  I demanded half of the profits.  She went banshee hag on me me, he cut me a check for half.

And that was the last interface I had with either of them.  Though I did run into my XILs a few times when we moved back to central Texas.  They kept inviting my bride and I and our son to heir Ranch for gamily gatherings. We never accepted those invitations.

I an now married and my DH and I dealt with this very very same thing while we were dating. I finally just told him that I wasn't going to be in a relationship where someone that's not a child is more important than I am. I know it sounds selfish, but I won't be in a relationship where I don't feel like I matter. If I'm going to be in a relationship for the rest of my life where I am taking care of someone else's children as my own, yet get reminded by everyone on a daily basis that I'm nothing more than a house maid to them, I refuse to be or made to feel unimportant to my DH. No offense to your SO but you deserve better and the only way that someone will treat you better is if you don't take no for an answer.