Children & the mistress

In 2 weeks steps toward my divorce start. First step is the custody of my 4 children. I'm so worried because my husband is living with his mistress and I do not want my children involved with that relationship just yet. My girls are 18 ,14,11, and 2. My husband thinks there is no issue with it but  all I see is issues. It's unhealthy.  It's also not sending the right message to the girls . His gf has her own 2 children who are young and if that's what she chooses to do with hers is fine. As for mine I'm not raising them to believe it's ok for a married man to be in another relationship.  What to do ?