BPDXW's new boyfriend too close to D12

[ProfDaddy]

I have primary custody of my children, S9 and D12.  BPDXW has the children EOW.  The xw has a new boyfriend, they have been steady for a few months.  S9 is away at a therapeutic boarding school this year, so xw is spending time with D12 alone.  I am concerned that someone I don't know is now sleeping in the same apartment as my D12 on her custody weekends.  I am further concerned that xw plans for him to supervise D12 alone over their week together on xmas break.  What have other parents done in this situation?  I don't want to be in the position of screening her boyfriends but need to keep D12 safe.  

[DreamGirl]

Couple questions:

Is this her first boyfriend post-divorce?

Do you trust your ex-wife's judgement?

What part is making you fearful?

Does your daughter have good boundaries?

[GaGrl]

Do you have a right of first refusal clause in your settlement?

[ProfDaddy]

Spoke with our family therapist about this issue.  My fiancee also spoke with friends and her T as well.  Everyone said they wouldn't leave their daughters alone with an adult man, especially when nobody knows much about him.  Polite email to ex got snarky reply about not my business to manage her household.  Safety of D12 is my business.

Best option I could find was to address a concern buried in ex's snarky email... .D12's best friend's parents probably busy.  So, I contacted another trusted friend's parents who have hosted D12 for slepovers.  They are glad to have D12 for a few days, so I arranged it and emailed the ex.