My ex's new boyfriend's criminal past

I am a father of a 5 & 1/2 year old daughter by a woman with whom I was not married (though I was previously and she was at the time we met). About 5 years ago we had a fairly long and vicious custody battle, ultimately resulting in joint legal custody, mom having “primary physical custody”, and me having “secondary physical custody”. Our case is extremely storied with too much detail to summarize here, but now after five years and through circumstances not entirely of her choosing (including a 2nd marriage and quick, subsequent separation, grandmother/caretaker moving away, and finally needing full-time employment), I am becoming more and more valuable for mom in raising our child. Consequently, I have made accommodations to her erratic schedule and other requests in order to achieve essentially a de-facto 50/50 custody split of our daughter. This has been since January of this year (2010).

The biggest issue with my ex at present is getting her to agree to a consent order to modify the existing custody order to one that more closely aligns with our current circumstances, i.e. “joint custody”. There’s other things involved in this too, but the custody time share is the biggest. She is agreeing to this in theory, but is also basically willing to lie about some other things she explicitly (and with conviction at the time) said she would do.

Anyway …
Roughly 3 months ago (May 2010) she started seeing and seriously dating a man who is in some some pretty heavy legal hot water. He has three domestic violence criminal charges pending against him (simple assault, assault on a female, and communicating threats) stemming from an incident in January with his wife and 15-year old son. He is in a “first-time offender’s” program which involves a deferred prosecution (basically admitting guilt for the promise of a future dismissal) pending compliance with certain classes and community service. His next court date has been set for 3/30/2011.

My question is (finally!):
Do I have any chance or leverage whatsoever in requesting some sort of restraining or “no contact” order with my daughter against this man?
My ex originally said, after she separated from her 2nd husband, that she was not going to introduce any new men to our daughter until she turns 18. I thought this was unrealistic of her to volunteer this, but she did and I think she was feeling at least a little remorse at attempting and basically admitting to “replacing” me and having some fears of a revolving door of men perception with our daughter … not a very good example. Now of course she’s fallen madly in love again and wants to pretend (i.e., LIE) that she never said any of this. I don’t trust this man and I want to protect my daughter. My ex has not been known to make very good decisions and is extremely capricious and transient. And oh, I forgot to mention that she also went through a deferred prosecution for a “simple” assault charge against me 5 years ago (which of course she takes no responsibility for and blames me).

Thank you for any advice or opinions you can offer.

You may file a motion to modify custody with the courts based on the changed circumstances since the entry of the last order. As part of your case you may present evidence of the dangerous nature of the man she is now seeing and the court may order that she not allow the child to be around him as part of a new custody order.