Dear Dave: You didn't define what the interaction with your ex-wife is. You mentioned having children together so I'm assuming the interaction has to do with them. Your new girlfriend has a lot to contend with. When she entered your life, she also entered the life of your children and your ex. The part that will make a difference, in whether your girlfriend stays or goes, is how you deal with your ex with respect to your girlfriend.
Ask yourself if you are interacting with your ex-wife at times that it has nothing to do with your children. Are there unresolved emotions that cause you to be around or talk to your ex-wife when you don't really have to? Do you find excuses to be around your ex-wife?
While your girlfriend might truly be jealous, it's possible she feels threatened by your interaction with your ex-wife if the interaction isn't reasonable. I say this because I know of too many cases where there are unresolved feelings and the person, without realizing it, finds excuses to be around the ex. They step in to help when the issue has nothing to do with the children, in a way that mimics when they were married.
Make sure your girlfriend knows she is the most important lady in your life. Don't step into your ex-wife's life if stepping in isn't justified. Communicate openly with your girlfriend to find out what she is feeling. Don't be defensive, but listen to what she has to say. If you haven't given her reason to be jealous, help her to work through her feelings.