Visitation concerns

My husband and I are separating after 19 years of on-and-off cheating.  Most recently, he has been seeing another woman since around Thanksgiving.  He is moving out (looking for a place now) with the other woman.  I am concerned about my kids having sleepover visitation at his new place with this new woman.  I don't want my kids to see him with another woman yet, they are dealing with enough trauma from the split (we kept our problems hidden well and our split is a shock to everyone).  I recently found out that in the other woman's divorce, she lost temporary custody to her husband.  I don't know any details, but this only adds to my concerns.  Am I being unreasonable?  My husband is not fighting me on it for the most part, but I can tell he's getting irritated.  I just believe that their relationship won't last (he's been through many "other women") and I don't want my kids to get to know her only to have their hearts broken AGAIN in a couple of months.  I don't know whether to just give in and help guide my kids through their experiences with them or to stick to my guns and keep asking him to have visitation away from his home or only when she is not there.  Help!