Fiancé has cheating behavior. Should he attend our family vacation?

My baby's Dad takes care of her so I can work. He's on disability and can't come up with the money on a whim. We always said we'd go in vacation for the baby's first vacation. Since being caught video sexting women. In numerous occasions with no plan to stop as i keep seeing I no longer sleep with him and it ruined our relationship.   My baby is 4 months I have two kids that are not his older . He so far has been a good dad . Should I pay for him to come and have him pay me back in installments ? Should I just go away just my kids and I? No matter what we have the arrangement that he stays at my place other room but here to help care for baby. I'm very hurt and confused. We're over but how do you do vacations with an ex parent .very recent break up.