Will try to be brief and to the point.

1. My wife gets very angry with me when I speak with my ex, even in regards to our two children from our marriage. Specifically when its not done with her in the room( which sometimes is impossible based on our work schedules and life in general).

2. My wife's ex is coming for a visit, she is excited because she wants to see what's going on with his life( she is telling me she wants to here if he's "struggling'). I asked if I could be present and she said no, he would only open up to her. I think this sends a bad message to him as in that she still cares for him and the such. Basically I see a double standard in which I adhere to here wishes about comm. With my ex, but she disregards my concerns and tells me to get over it.

She had better get over it ! Yes it is a double standard and she is being very insecure and immature in her reasoning. You and your ex still share a very important bond, your two children. She has to realize that. Does she not have any children with her ex that she has brought to her marriage with you ?

You two have to sit down and arrange some ground rules without getting into an argument about this. Your ex, the biological mother of your children, still has a viable opinion in their upbringing.

Tick

To add to what Tickle said, not only is it a double standard, but what she is planning could be seen worse because she wants to 'comfort' him in his time of 'need'. It isn't healthy for their relationship or yours with her.

Is there a reason other than jealousy or general insecurity causing her to not trust you being alone with your ex?

You need to sit down together and discuss both issues. Work together to set boundaries and compromises for both of you. If needed, maybe get a third person like a marriage counselor to mediate the discussion.

Do you always wimp out to your wife when she is both unreasonable, and unfair? She is crossing her own boundaries that she has set for you.

You have children with your ex, and will for at least till they are out of the home, but really for the rest of your life share some things with her, birth of grandkids, or their marriage and so on.
Wait till they want you to set with ex at the wedding.

She needs to learn she can not have her way and if she does not trust you, there are more or other issues to deal with.